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Solve the following coding problem using the programming language python:
There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru.
You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where:
<hostname> — server name (consists of words and maybe some dots separating them), /<path> — optional part, where <path> consists of words separated by slashes.
We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications.
Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name.
Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different.
-----Input-----
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of page queries. Then follow n lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where:
<hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20. <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20.
Addresses are not guaranteed to be distinct.
-----Output-----
First print k — the number of groups of server names that correspond to one website. You should count only groups of size greater than one.
Next k lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order.
-----Examples-----
Input
10
http://abacaba.ru/test
http://abacaba.ru/
http://abacaba.com
http://abacaba.com/test
http://abacaba.de/
http://abacaba.ru/test
http://abacaba.de/test
http://abacaba.com/
http://abacaba.com/t
http://abacaba.com/test
Output
1
http://abacaba.de http://abacaba.ru
Input
14
http://c
http://ccc.bbbb/aba..b
http://cba.com
http://a.c/aba..b/a
http://abc/
http://a.c/
http://ccc.bbbb
http://ab.ac.bc.aa/
http://a.a.a/
http://ccc.bbbb/
http://cba.com/
http://cba.com/aba..b
http://a.a.a/aba..b/a
http://abc/aba..b/a
Output
2
http://cba.com http://ccc.bbbb
http://a.a.a http://a.c http://abc
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\n# Bartek Kostka\n# You are not prepared!\n\n#include \"bits/stdc++.h\"\n\nn = int(input())\nW = {}\nfor i in range(n):\n adr = input()\n adr = adr.split(\"/\")\n if adr[-1] == '':\n adr[-1] = '?'\n domena = \"/\".join(adr[:3])\n adres = \"/\".join(adr[3:])\n #print(domena, adres)\n if domena not in W:\n W[domena] = set()\n W[domena].add(adres)\n\nE = {}\nfor key, ele in list(W.items()):\n #print(key, ele)\n lele = \"#\".join(sorted(list(ele)))\n if lele not in E:\n E[lele] = []\n E[lele].append(key)\n\nres = 0\nfor key, ele in list(E.items()):\n if len(ele) > 1:\n res += 1\n\nprint(res)\nfor key, ele in list(E.items()):\n if len(ele) > 1:\n print(\" \".join(ele))\n\n```"
] |
[{"type": "stdin_stdout", "input": "10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test\n", "output": "1\nhttp://abacaba.de http://abacaba.ru \n"}, {"type": "stdin_stdout", "input": "14\nhttp://c\nhttp://ccc.bbbb/aba..b\nhttp://cba.com\nhttp://a.c/aba..b/a\nhttp://abc/\nhttp://a.c/\nhttp://ccc.bbbb\nhttp://ab.ac.bc.aa/\nhttp://a.a.a/\nhttp://ccc.bbbb/\nhttp://cba.com/\nhttp://cba.com/aba..b\nhttp://a.a.a/aba..b/a\nhttp://abc/aba..b/a\n", "output": "2\nhttp://cba.com http://ccc.bbbb \nhttp://a.a.a http://a.c http://abc \n"}, {"type": "stdin_stdout", "input": "10\nhttp://tqr.ekdb.nh/w\nhttp://p.ulz/ifw\nhttp://w.gw.dw.xn/kpe\nhttp://byt.mqii.zkv/j/xt\nhttp://ovquj.rbgrlw/k..\nhttp://bv.plu.e.dslg/j/xt\nhttp://udgci.ufgi.gwbd.s/\nhttp://l.oh.ne.o.r/.vo\nhttp://l.oh.ne.o.r/w\nhttp://tqr.ekdb.nh/.vo\n", "output": "2\nhttp://l.oh.ne.o.r http://tqr.ekdb.nh \nhttp://bv.plu.e.dslg http://byt.mqii.zkv \n"}, {"type": "stdin_stdout", "input": "12\nhttp://ickght.ck/mr\nhttp://a.exhel/.b\nhttp://a.exhel/\nhttp://ti.cdm/\nhttp://ti.cdm/x/wd/lm.h.\nhttp://ickght.ck/a\nhttp://ickght.ck\nhttp://c.gcnk.d/.b\nhttp://c.gcnk.d/x/wd/lm.h.\nhttp://ti.cdm/.b\nhttp://a.exhel/x/wd/lm.h.\nhttp://c.gcnk.d/\n", "output": "1\nhttp://a.exhel http://c.gcnk.d http://ti.cdm \n"}, {"type": "stdin_stdout", "input": "14\nhttp://jr/kgb\nhttp://ps.p.t.jeua.x.a.q.t\nhttp://gsqqs.n/t/\nhttp://w.afwsnuc.ff.km/cohox/u.\nhttp://u.s.wbumkuqm/\nhttp://u.s.wbumkuqm/cohox/u.\nhttp://nq.dzjkjcwv.f.s/bvm/\nhttp://zoy.shgg\nhttp://gsqqs.n\nhttp://u.s.wbumkuqm/b.pd.\nhttp://w.afwsnuc.ff.km/\nhttp://w.afwsnuc.ff.km/b.pd.\nhttp://nq.dzjkjcwv.f.s/n\nhttp://nq.dzjkjcwv.f.s/ldbw\n", "output": "2\nhttp://ps.p.t.jeua.x.a.q.t http://zoy.shgg \nhttp://u.s.wbumkuqm http://w.afwsnuc.ff.km \n"}, {"type": "stdin_stdout", "input": "15\nhttp://l.edzplwqsij.rw/\nhttp://m.e.mehd.acsoinzm/s\nhttp://yg.ttahn.xin.obgez/ap/\nhttp://qqbb.pqkaqcncodxmaae\nhttp://lzi.a.flkp.lnn.k/o/qfr.cp\nhttp://lzi.a.flkp.lnn.k/f\nhttp://p.ngu.gkoq/.szinwwi\nhttp://qqbb.pqkaqcncodxmaae/od\nhttp://qqbb.pqkaqcncodxmaae\nhttp://wsxvmi.qpe.fihtgdvi/e./\nhttp://p.ngu.gkoq/zfoh\nhttp://m.e.mehd.acsoinzm/xp\nhttp://c.gy.p.h.tkrxt.jnsjt/j\nhttp://wsxvmi.qpe.fihtgdvi/grkag.z\nhttp://p.ngu.gkoq/t\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "15\nhttp://w.hhjvdn.mmu/.ca.p\nhttp://m.p.p.lar/\nhttp://lgmjun.r.kogpr.ijn/./t\nhttp://bapchpl.mcw.a.lob/d/ym/./g.q\nhttp://uxnjfnjp.kxr.ss.e.uu/jwo./hjl/\nhttp://fd.ezw.ykbb.xhl.t/\nhttp://i.xcb.kr/.ca.p\nhttp://jofec.ry.fht.gt\nhttp://qeo.gghwe.lcr/d/ym/./g.q\nhttp://gt\nhttp://gjvifpf.d/d/ym/./g.q\nhttp://oba\nhttp://rjs.qwd/v/hi\nhttp://fgkj/\nhttp://ivun.naumc.l/.ca.p\n", "output": "4\nhttp://gt http://jofec.ry.fht.gt http://oba \nhttp://fd.ezw.ykbb.xhl.t http://fgkj http://m.p.p.lar \nhttp://i.xcb.kr http://ivun.naumc.l http://w.hhjvdn.mmu \nhttp://bapchpl.mcw.a.lob http://gjvifpf.d http://qeo.gghwe.lcr \n"}, {"type": "stdin_stdout", "input": "20\nhttp://gjwr/xsoiagp/\nhttp://gdnmu/j\nhttp://yfygudx.e.aqa.ezh/j\nhttp://mpjxue.cuvipq/\nhttp://a/\nhttp://kr/..n/c.\nhttp://a/xsoiagp/\nhttp://kr/z\nhttp://kr/v.cv/rk/k\nhttp://lvhpz\nhttp://qv.v.jqzhq\nhttp://y.no/\nhttp://kr/n\nhttp://y.no/xsoiagp/\nhttp://kr/ebe/z/\nhttp://olsvbxxw.win.n/j\nhttp://p.ct/j\nhttp://mpjxue.cuvipq/xsoiagp/\nhttp://kr/j\nhttp://gjwr/\n", "output": "3\nhttp://lvhpz http://qv.v.jqzhq \nhttp://a http://gjwr http://mpjxue.cuvipq http://y.no \nhttp://gdnmu http://olsvbxxw.win.n http://p.ct http://yfygudx.e.aqa.ezh \n"}, {"type": "stdin_stdout", "input": "1\nhttp://a\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "1\nhttp://a.a.a.f.r.f.q.e.w.a/fwe..sdfv....\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "3\nhttp://abacaba.com/test\nhttp://abacaba.de/test\nhttp://abacaba.de/test\n", "output": "1\nhttp://abacaba.com http://abacaba.de \n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru.
You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where:
<hostname> — server name (consists of words and maybe some dots separating them), /<path> — optional part, where <path> consists of words separated by slashes.
We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications.
Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name.
Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different.
-----Input-----
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of page queries. Then follow n lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where:
<hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20. <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20.
Addresses are not guaranteed to be distinct.
-----Output-----
First print k — the number of groups of server names that correspond to one website. You should count only groups of size greater than one.
Next k lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order.
-----Examples-----
Input
10
http://abacaba.ru/test
http://abacaba.ru/
http://abacaba.com
http://abacaba.com/test
http://abacaba.de/
http://abacaba.ru/test
http://abacaba.de/test
http://abacaba.com/
http://abacaba.com/t
http://abacaba.com/test
Output
1
http://abacaba.de http://abacaba.ru
Input
14
http://c
http://ccc.bbbb/aba..b
http://cba.com
http://a.c/aba..b/a
http://abc/
http://a.c/
http://ccc.bbbb
http://ab.ac.bc.aa/
http://a.a.a/
http://ccc.bbbb/
http://cba.com/
http://cba.com/aba..b
http://a.a.a/aba..b/a
http://abc/aba..b/a
Output
2
http://cba.com http://ccc.bbbb
http://a.a.a http://a.c http://abc
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
[{"type": "stdin_stdout", "input": "10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test\n", "output": "1\nhttp://abacaba.de http://abacaba.ru \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\nhttp://c\nhttp://ccc.bbbb/aba..b\nhttp://cba.com\nhttp://a.c/aba..b/a\nhttp://abc/\nhttp://a.c/\nhttp://ccc.bbbb\nhttp://ab.ac.bc.aa/\nhttp://a.a.a/\nhttp://ccc.bbbb/\nhttp://cba.com/\nhttp://cba.com/aba..b\nhttp://a.a.a/aba..b/a\nhttp://abc/aba..b/a\n", "output": "2\nhttp://cba.com http://ccc.bbbb \nhttp://a.a.a http://a.c http://abc \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\nhttp://tqr.ekdb.nh/w\nhttp://p.ulz/ifw\nhttp://w.gw.dw.xn/kpe\nhttp://byt.mqii.zkv/j/xt\nhttp://ovquj.rbgrlw/k..\nhttp://bv.plu.e.dslg/j/xt\nhttp://udgci.ufgi.gwbd.s/\nhttp://l.oh.ne.o.r/.vo\nhttp://l.oh.ne.o.r/w\nhttp://tqr.ekdb.nh/.vo\n", "output": "2\nhttp://l.oh.ne.o.r http://tqr.ekdb.nh \nhttp://bv.plu.e.dslg http://byt.mqii.zkv \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "12\nhttp://ickght.ck/mr\nhttp://a.exhel/.b\nhttp://a.exhel/\nhttp://ti.cdm/\nhttp://ti.cdm/x/wd/lm.h.\nhttp://ickght.ck/a\nhttp://ickght.ck\nhttp://c.gcnk.d/.b\nhttp://c.gcnk.d/x/wd/lm.h.\nhttp://ti.cdm/.b\nhttp://a.exhel/x/wd/lm.h.\nhttp://c.gcnk.d/\n", "output": "1\nhttp://a.exhel http://c.gcnk.d http://ti.cdm \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\nhttp://jr/kgb\nhttp://ps.p.t.jeua.x.a.q.t\nhttp://gsqqs.n/t/\nhttp://w.afwsnuc.ff.km/cohox/u.\nhttp://u.s.wbumkuqm/\nhttp://u.s.wbumkuqm/cohox/u.\nhttp://nq.dzjkjcwv.f.s/bvm/\nhttp://zoy.shgg\nhttp://gsqqs.n\nhttp://u.s.wbumkuqm/b.pd.\nhttp://w.afwsnuc.ff.km/\nhttp://w.afwsnuc.ff.km/b.pd.\nhttp://nq.dzjkjcwv.f.s/n\nhttp://nq.dzjkjcwv.f.s/ldbw\n", "output": "2\nhttp://ps.p.t.jeua.x.a.q.t http://zoy.shgg \nhttp://u.s.wbumkuqm http://w.afwsnuc.ff.km \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\nhttp://l.edzplwqsij.rw/\nhttp://m.e.mehd.acsoinzm/s\nhttp://yg.ttahn.xin.obgez/ap/\nhttp://qqbb.pqkaqcncodxmaae\nhttp://lzi.a.flkp.lnn.k/o/qfr.cp\nhttp://lzi.a.flkp.lnn.k/f\nhttp://p.ngu.gkoq/.szinwwi\nhttp://qqbb.pqkaqcncodxmaae/od\nhttp://qqbb.pqkaqcncodxmaae\nhttp://wsxvmi.qpe.fihtgdvi/e./\nhttp://p.ngu.gkoq/zfoh\nhttp://m.e.mehd.acsoinzm/xp\nhttp://c.gy.p.h.tkrxt.jnsjt/j\nhttp://wsxvmi.qpe.fihtgdvi/grkag.z\nhttp://p.ngu.gkoq/t\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\nhttp://w.hhjvdn.mmu/.ca.p\nhttp://m.p.p.lar/\nhttp://lgmjun.r.kogpr.ijn/./t\nhttp://bapchpl.mcw.a.lob/d/ym/./g.q\nhttp://uxnjfnjp.kxr.ss.e.uu/jwo./hjl/\nhttp://fd.ezw.ykbb.xhl.t/\nhttp://i.xcb.kr/.ca.p\nhttp://jofec.ry.fht.gt\nhttp://qeo.gghwe.lcr/d/ym/./g.q\nhttp://gt\nhttp://gjvifpf.d/d/ym/./g.q\nhttp://oba\nhttp://rjs.qwd/v/hi\nhttp://fgkj/\nhttp://ivun.naumc.l/.ca.p\n", "output": "4\nhttp://gt http://jofec.ry.fht.gt http://oba \nhttp://fd.ezw.ykbb.xhl.t http://fgkj http://m.p.p.lar \nhttp://i.xcb.kr http://ivun.naumc.l http://w.hhjvdn.mmu \nhttp://bapchpl.mcw.a.lob http://gjvifpf.d http://qeo.gghwe.lcr \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "20\nhttp://gjwr/xsoiagp/\nhttp://gdnmu/j\nhttp://yfygudx.e.aqa.ezh/j\nhttp://mpjxue.cuvipq/\nhttp://a/\nhttp://kr/..n/c.\nhttp://a/xsoiagp/\nhttp://kr/z\nhttp://kr/v.cv/rk/k\nhttp://lvhpz\nhttp://qv.v.jqzhq\nhttp://y.no/\nhttp://kr/n\nhttp://y.no/xsoiagp/\nhttp://kr/ebe/z/\nhttp://olsvbxxw.win.n/j\nhttp://p.ct/j\nhttp://mpjxue.cuvipq/xsoiagp/\nhttp://kr/j\nhttp://gjwr/\n", "output": "3\nhttp://lvhpz http://qv.v.jqzhq \nhttp://a http://gjwr http://mpjxue.cuvipq http://y.no \nhttp://gdnmu http://olsvbxxw.win.n http://p.ct http://yfygudx.e.aqa.ezh \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\nhttp://a\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\nhttp://a.a.a.f.r.f.q.e.w.a/fwe..sdfv....\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\nhttp://abacaba.com/test\nhttp://abacaba.de/test\nhttp://abacaba.de/test\n", "output": "1\nhttp://abacaba.com http://abacaba.de \n", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_0
| 0
|
[
{
"answer": "```python\nimport math\nimport re\nfrom fractions import Fraction\nfrom collections import Counter\n\nclass Task:\n ips = []\n k = 0\n answer = ''\n \n def __init__(self):\n n, self.k = [int(x) for x in input().split()]\n self.ips = ['' for _ in range(n)]\n for i in range(len(self.ips)):\n self.ips[i] = input()\n\n def solve(self):\n ips, k = self.ips, self.k\n ipAsNumbers = []\n for currentIp in ips:\n number = 0\n parts = currentIp.split('.')\n for i in range(0, len(parts)):\n number += int(parts[i]) * 2**(32 - (i + 1) * 8)\n ipAsNumbers += [number]\n\n mask = 0\n for i in range(31, -1, -1):\n mask += 2**i\n netAddresses = set()\n for ip in ipAsNumbers:\n netAddresses.add(mask & ip)\n if len(netAddresses) == k:\n mask = bin(mask)[2:]\n self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\n for i in range(0, len(mask), 8)])\n return\n self.answer = '-1'\n\n\n def printAnswer(self):\n print(self.answer)\n #for line in self.answer:\n # print(line)\n\ntask = Task()\ntask.solve()\ntask.printAnswer()\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nThe problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
},
{
"answer": "```python\nimport sys\n(n, k) = map(int, input().split())\nmvals = []\nfor _ in range(n):\n\t(x, y, z, w) = map(int, input().split('.'))\n\tmvals.append(x << 24 | y << 16 | z << 8 | w)\nmv = (1 << 32) - 1\nfor ind in range(31, 0, -1):\n\tst = set()\n\tmask = mv - ((1 << ind) - 1)\n\tfor i in range(n):\n\t\tst.add(mask & mvals[i])\n\tif len(st) == k:\n\t\t(x, y, z, w) = (mask >> 24, (mask >> 16) % 256, (mask >> 8) % 256, mask % 256)\n\t\tprint(f'{str(x)}.{str(y)}.{str(z)}.{str(w)}')\n\t\texit()\nprint(-1)\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nThe problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
},
{
"answer": "```python\ndef f(t):\n a, b, c, d = map(int, t.split('.'))\n return d + (c << 8) + (b << 16) + (a << 24)\n\ndef g(x):\n p = [0] * 4\n for i in range(4):\n p[3 - i] = str(x % 256)\n x //= 256\n return '.'.join(p)\n\nn, k = map(int, input().split())\nt = [f(input()) for i in range(n)]\np = [0] * n\nx = 1 << 31\nfor i in range(32):\n for j, y in enumerate(t):\n if y & x: p[j] += x\n if len(set(p)) >= k: break\n x >>= 1\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\n```",
"question": "Solve the following coding problem using the programming language python:\n\nThe problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\nInput\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 105) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\nOutput\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\nExamples\n\nInput\n\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\n\nOutput\n\n255.255.254.0\n\nInput\n\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\n\nOutput\n\n255.255.0.0\n\nInput\n\n2 1\n255.0.0.1\n0.0.0.2\n\n\nOutput\n\n-1\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
}
] |
Solve the following coding problem using the programming language python:
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if $\operatorname{mod}(x, b) \neq 0$ and $\frac{\operatorname{div}(x, b)}{\operatorname{mod}(x, b)} = k$, where k is some integer number in range [1, a].
By $\operatorname{div}(x, y)$ we denote the quotient of integer division of x and y. By $\operatorname{mod}(x, y)$ we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (10^9 + 7). Can you compute it faster than Dreamoon?
-----Input-----
The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10^7).
-----Output-----
Print a single integer representing the answer modulo 1 000 000 007 (10^9 + 7).
-----Examples-----
Input
1 1
Output
0
Input
2 2
Output
8
-----Note-----
For the first sample, there are no nice integers because $\operatorname{mod}(x, 1)$ is always zero.
For the second sample, the set of nice integers is {3, 5}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\na,b=map(int,input().split())\nprint(((b-1)*a*b//2+(a+1)*a*b*b*(b-1)//4)%1000000007)\n```"
] |
[{"type": "stdin_stdout", "input": "1 1\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "2 2\n", "output": "8\n"}, {"type": "stdin_stdout", "input": "4 1\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "4 2\n", "output": "24\n"}, {"type": "stdin_stdout", "input": "4 3\n", "output": "102\n"}, {"type": "stdin_stdout", "input": "4 4\n", "output": "264\n"}, {"type": "stdin_stdout", "input": "3 4\n", "output": "162\n"}, {"type": "stdin_stdout", "input": "2 4\n", "output": "84\n"}, {"type": "stdin_stdout", "input": "1 4\n", "output": "30\n"}, {"type": "stdin_stdout", "input": "1000 1000\n", "output": "247750000\n"}, {"type": "stdin_stdout", "input": "10000000 10000000\n", "output": "425362313\n"}, {"type": "stdin_stdout", "input": "10000000 9999999\n", "output": "930564389\n"}, {"type": "stdin_stdout", "input": "2 10000000\n", "output": "990423507\n"}, {"type": "stdin_stdout", "input": "10000000 2\n", "output": "19300000\n"}, {"type": "stdin_stdout", "input": "9999999 2\n", "output": "999300006\n"}, {"type": "stdin_stdout", "input": "9999999 9999999\n", "output": "957764103\n"}, {"type": "stdin_stdout", "input": "10000000 10000\n", "output": "723127969\n"}, {"type": "stdin_stdout", "input": "10000 10000000\n", "output": "372369289\n"}, {"type": "stdin_stdout", "input": "2 9999999\n", "output": "48573499\n"}, {"type": "stdin_stdout", "input": "123456 123456\n", "output": "417111819\n"}, {"type": "stdin_stdout", "input": "6407688 3000816\n", "output": "895399645\n"}, {"type": "stdin_stdout", "input": "9956532 1084240\n", "output": "554368769\n"}, {"type": "stdin_stdout", "input": "3505377 9167664\n", "output": "80435138\n"}, {"type": "stdin_stdout", "input": "7054221 7251088\n", "output": "7849970\n"}, {"type": "stdin_stdout", "input": "346169 367216\n", "output": "358144298\n"}, {"type": "stdin_stdout", "input": "3895014 8450640\n", "output": "627604019\n"}, {"type": "stdin_stdout", "input": "861392 6200826\n", "output": "180835815\n"}, {"type": "stdin_stdout", "input": "4410236 9316955\n", "output": "602743722\n"}, {"type": "stdin_stdout", "input": "2926377 2367675\n", "output": "395740917\n"}, {"type": "stdin_stdout", "input": "1507925 5483803\n", "output": "727607740\n"}, {"type": "stdin_stdout", "input": "9832578 8599931\n", "output": "428281878\n"}, {"type": "stdin_stdout", "input": "8348718 6683355\n", "output": "275994807\n"}, {"type": "stdin_stdout", "input": "1897562 4766779\n", "output": "148050609\n"}, {"type": "stdin_stdout", "input": "413703 2850203\n", "output": "76966774\n"}, {"type": "stdin_stdout", "input": "8995251 5966331\n", "output": "451718548\n"}, {"type": "stdin_stdout", "input": "7319903 9017051\n", "output": "975259203\n"}, {"type": "stdin_stdout", "input": "9253578 1799941\n", "output": "868664771\n"}, {"type": "stdin_stdout", "input": "7835126 9883365\n", "output": "119844544\n"}, {"type": "stdin_stdout", "input": "6351267 7966789\n", "output": "683811063\n"}, {"type": "stdin_stdout", "input": "9900111 1082917\n", "output": "539539383\n"}, {"type": "stdin_stdout", "input": "1 10000000\n", "output": "995024507\n"}, {"type": "stdin_stdout", "input": "123456 234567\n", "output": "93010021\n"}, {"type": "stdin_stdout", "input": "888888 888888\n", "output": "456888843\n"}, {"type": "stdin_stdout", "input": "1001 1500126\n", "output": "45074025\n"}, {"type": "stdin_stdout", "input": "9243243 432434\n", "output": "203891513\n"}, {"type": "stdin_stdout", "input": "3 10000000\n", "output": "986197007\n"}, {"type": "stdin_stdout", "input": "4108931 211273\n", "output": "142398939\n"}, {"type": "stdin_stdout", "input": "999999 92321\n", "output": "286549418\n"}, {"type": "stdin_stdout", "input": "999999 999999\n", "output": "691690639\n"}, {"type": "stdin_stdout", "input": "191919 123123\n", "output": "358196438\n"}, {"type": "stdin_stdout", "input": "999999 1000000\n", "output": "725921292\n"}, {"type": "stdin_stdout", "input": "31623 10000000\n", "output": "382702377\n"}, {"type": "stdin_stdout", "input": "1000023 1000043\n", "output": "175442768\n"}, {"type": "stdin_stdout", "input": "666666 666666\n", "output": "869302791\n"}, {"type": "stdin_stdout", "input": "7672285 753250\n", "output": "461773059\n"}, {"type": "stdin_stdout", "input": "1000000 1000000\n", "output": "249917764\n"}, {"type": "stdin_stdout", "input": "6340794 6874449\n", "output": "930977735\n"}, {"type": "stdin_stdout", "input": "9998486 9998486\n", "output": "988877388\n"}, {"type": "stdin_stdout", "input": "9999997 9999998\n", "output": "946983076\n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if $\operatorname{mod}(x, b) \neq 0$ and $\frac{\operatorname{div}(x, b)}{\operatorname{mod}(x, b)} = k$, where k is some integer number in range [1, a].
By $\operatorname{div}(x, y)$ we denote the quotient of integer division of x and y. By $\operatorname{mod}(x, y)$ we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (10^9 + 7). Can you compute it faster than Dreamoon?
-----Input-----
The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10^7).
-----Output-----
Print a single integer representing the answer modulo 1 000 000 007 (10^9 + 7).
-----Examples-----
Input
1 1
Output
0
Input
2 2
Output
8
-----Note-----
For the first sample, there are no nice integers because $\operatorname{mod}(x, 1)$ is always zero.
For the second sample, the set of nice integers is {3, 5}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
[{"type": "stdin_stdout", "input": "1 1\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 2\n", "output": "8\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 1\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 2\n", "output": "24\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 3\n", "output": "102\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 4\n", "output": "264\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 4\n", "output": "162\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 4\n", "output": "84\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 4\n", "output": "30\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000 1000\n", "output": "247750000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000000 10000000\n", "output": "425362313\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000000 9999999\n", "output": "930564389\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 10000000\n", "output": "990423507\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000000 2\n", "output": "19300000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9999999 2\n", "output": "999300006\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9999999 9999999\n", "output": "957764103\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000000 10000\n", "output": "723127969\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000 10000000\n", "output": "372369289\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 9999999\n", "output": "48573499\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "123456 123456\n", "output": "417111819\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6407688 3000816\n", "output": "895399645\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9956532 1084240\n", "output": "554368769\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3505377 9167664\n", "output": "80435138\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7054221 7251088\n", "output": "7849970\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "346169 367216\n", "output": "358144298\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3895014 8450640\n", "output": "627604019\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "861392 6200826\n", "output": "180835815\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4410236 9316955\n", "output": "602743722\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2926377 2367675\n", "output": "395740917\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1507925 5483803\n", "output": "727607740\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9832578 8599931\n", "output": "428281878\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "8348718 6683355\n", "output": "275994807\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1897562 4766779\n", "output": "148050609\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "413703 2850203\n", "output": "76966774\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "8995251 5966331\n", "output": "451718548\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7319903 9017051\n", "output": "975259203\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9253578 1799941\n", "output": "868664771\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7835126 9883365\n", "output": "119844544\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6351267 7966789\n", "output": "683811063\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9900111 1082917\n", "output": "539539383\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 10000000\n", "output": "995024507\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "123456 234567\n", "output": "93010021\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "888888 888888\n", "output": "456888843\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1001 1500126\n", "output": "45074025\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9243243 432434\n", "output": "203891513\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 10000000\n", "output": "986197007\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4108931 211273\n", "output": "142398939\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 92321\n", "output": "286549418\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 999999\n", "output": "691690639\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "191919 123123\n", "output": "358196438\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 1000000\n", "output": "725921292\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "31623 10000000\n", "output": "382702377\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000023 1000043\n", "output": "175442768\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "666666 666666\n", "output": "869302791\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7672285 753250\n", "output": "461773059\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000000 1000000\n", "output": "249917764\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6340794 6874449\n", "output": "930977735\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9998486 9998486\n", "output": "988877388\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9999997 9999998\n", "output": "946983076\n", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_1
| 1
|
[
{
"answer": "```python\nimport sys\nimport math\nMAXNUM = math.inf\nMINNUM = -1 * math.inf\nASCIILOWER = 97\nASCIIUPPER = 65\nMODMAX = 1000000007\n\ndef getInt():\n\treturn int(sys.stdin.readline().rstrip())\n\ndef getInts():\n\treturn map(int, sys.stdin.readline().rstrip().split(' '))\n\ndef getString():\n\treturn sys.stdin.readline().rstrip()\n\ndef printOutput(ans):\n\tsys.stdout.write()\n\tpass\n\ndef termadd(n):\n\treturn n * (n + 1) // 2\n\ndef solve(a, b):\n\treturn a * (b - 1) * b * (b * (a + 1) + 2) // 4 % MODMAX\n\ndef readinput():\n\t(a, b) = getInts()\n\tprint(solve(a, b))\nreadinput()\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nDreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].\n\nBy <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.\n\nThe answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?\n\nInput\n\nThe single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).\n\nOutput\n\nPrint a single integer representing the answer modulo 1 000 000 007 (109 + 7).\n\nExamples\n\nInput\n\n1 1\n\n\nOutput\n\n0\n\n\nInput\n\n2 2\n\n\nOutput\n\n8\n\nNote\n\nFor the first sample, there are no nice integers because <image> is always zero.\n\nFor the second sample, the set of nice integers is {3, 5}.\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
},
{
"answer": "```python\na, b = (input()).split(' ')\n\na = int(a)\nb=int(b)\n\nresult = a*b*(b-1)*(a*b+b+2)//4\n#result = int(result)\nresult = result % ( 10**9 +7)\nprint((result))\n```",
"question": "Solve the following coding problem using the programming language python:\n\nDreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].\n\nBy <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.\n\nThe answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?\n\nInput\n\nThe single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).\n\nOutput\n\nPrint a single integer representing the answer modulo 1 000 000 007 (109 + 7).\n\nExamples\n\nInput\n\n1 1\n\n\nOutput\n\n0\n\n\nInput\n\n2 2\n\n\nOutput\n\n8\n\nNote\n\nFor the first sample, there are no nice integers because <image> is always zero.\n\nFor the second sample, the set of nice integers is {3, 5}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "```python\nimport sys\nimport math\n\nMAXNUM = math.inf\nMINNUM = -1 * math.inf\nASCIILOWER = 97\nASCIIUPPER = 65\nMODMAX = 1000000007\n\n\ndef getInt():\n return int(sys.stdin.readline().rstrip())\n\n\ndef getInts():\n return map(int, sys.stdin.readline().rstrip().split(\" \"))\n\n\ndef getString():\n return sys.stdin.readline().rstrip()\n\n\ndef printOutput(ans):\n sys.stdout.write()\n pass\n\n\ndef termadd(n):\n return (n * (n + 1)) // 2\n\n\ndef solve(a, b):\n return ((a*(b-1)*(b)*(b*(a+1) + 2))//4) % MODMAX\n\ndef readinput():\n a, b = getInts()\n print(solve(a, b))\n\n\nreadinput()\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nDreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].\n\nBy <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.\n\nThe answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?\n\nInput\n\nThe single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).\n\nOutput\n\nPrint a single integer representing the answer modulo 1 000 000 007 (109 + 7).\n\nExamples\n\nInput\n\n1 1\n\n\nOutput\n\n0\n\n\nInput\n\n2 2\n\n\nOutput\n\n8\n\nNote\n\nFor the first sample, there are no nice integers because <image> is always zero.\n\nFor the second sample, the set of nice integers is {3, 5}.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
}
] |
Solve the following coding problem using the programming language python:
Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.
You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.
Solve the problem to show that it's not a NP problem.
-----Input-----
The first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9).
-----Output-----
Print single integer, the integer that appears maximum number of times in the divisors.
If there are multiple answers, print any of them.
-----Examples-----
Input
19 29
Output
2
Input
3 6
Output
3
-----Note-----
Definition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html
The first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.
The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\nl,r = map(int, input().split(\" \"))\nif l == r:\n print (l)\nelse:\n print (2)\n```"
] |
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"stdin_stdout", "input": "908580370 968054552\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "951594860 953554446\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "347877978 913527175\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "620769961 988145114\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "820844234 892579936\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "741254764 741254768\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "80270976 80270977\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "392602363 392602367\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "519002744 519002744\n", "output": "519002744\n"}, {"type": "stdin_stdout", "input": "331900277 331900277\n", "output": "331900277\n"}, {"type": "stdin_stdout", "input": "419873015 419873018\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "349533413 349533413\n", "output": "349533413\n"}, {"type": "stdin_stdout", "input": "28829775 28829776\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "568814539 568814539\n", "output": "568814539\n"}, {"type": "stdin_stdout", "input": "720270740 720270743\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "871232720 871232722\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "305693653 305693653\n", "output": "305693653\n"}, {"type": "stdin_stdout", "input": "634097178 634097179\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "450868287 450868290\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "252662256 252662260\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "575062045 575062049\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "273072892 273072894\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "770439256 770439256\n", "output": "770439256\n"}, {"type": "stdin_stdout", "input": "2 1000000000\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "6 8\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "2 879190747\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "5 5\n", "output": "5\n"}, {"type": "stdin_stdout", "input": "999999937 999999937\n", "output": "999999937\n"}, {"type": "stdin_stdout", "input": "3 3\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "5 100\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "2 2\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "3 18\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "7 7\n", "output": "7\n"}, {"type": "stdin_stdout", "input": "39916801 39916801\n", "output": "39916801\n"}, {"type": "stdin_stdout", "input": "3 8\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "13 13\n", "output": "13\n"}, {"type": "stdin_stdout", "input": "4 8\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "3 12\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "6 12\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "999999103 999999103\n", "output": "999999103\n"}, {"type": "stdin_stdout", "input": "100000007 100000007\n", "output": "100000007\n"}, {"type": "stdin_stdout", "input": "3 99\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "999999733 999999733\n", "output": "999999733\n"}, {"type": "stdin_stdout", "input": "5 10\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "982451653 982451653\n", "output": "982451653\n"}, {"type": "stdin_stdout", "input": "999900001 1000000000\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "999727999 999727999\n", "output": "999727999\n"}, {"type": "stdin_stdout", "input": "2 999999999\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "242 244\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "3 10\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "15 27\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "998244353 998244353\n", "output": "998244353\n"}, {"type": "stdin_stdout", "input": "5 15\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "999999797 999999797\n", "output": "999999797\n"}, {"type": "stdin_stdout", "input": "2 3\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "999999929 999999929\n", "output": "999999929\n"}, {"type": "stdin_stdout", "input": "3 111111\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "12 18\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "479001599 479001599\n", "output": "479001599\n"}, {"type": "stdin_stdout", "input": "10000019 10000019\n", "output": "10000019\n"}, {"type": "stdin_stdout", "input": "715827883 715827883\n", "output": "715827883\n"}, {"type": "stdin_stdout", "input": "999992977 999992977\n", "output": "999992977\n"}, {"type": "stdin_stdout", "input": "11 11\n", "output": "11\n"}, {"type": "stdin_stdout", "input": "29 29\n", "output": "29\n"}, {"type": "stdin_stdout", "input": "1000003 1000003\n", "output": "1000003\n"}, {"type": "stdin_stdout", "input": "6 15\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "1200007 1200007\n", "output": "1200007\n"}, {"type": "stdin_stdout", "input": "3 1000000000\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "990000023 990000023\n", "output": "990000023\n"}, {"type": "stdin_stdout", "input": "1717 1717\n", "output": "1717\n"}, {"type": "stdin_stdout", "input": "141650963 141650963\n", "output": "141650963\n"}, {"type": "stdin_stdout", "input": "1002523 1002523\n", "output": "1002523\n"}, {"type": "stdin_stdout", "input": "900000011 900000011\n", "output": "900000011\n"}, {"type": "stdin_stdout", "input": "104729 104729\n", "output": "104729\n"}, {"type": "stdin_stdout", "input": "4 12\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "100003 100003\n", "output": "100003\n"}, {"type": "stdin_stdout", "input": "17 17\n", "output": "17\n"}, {"type": "stdin_stdout", "input": "10 100\n", "output": "2\n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.
You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.
Solve the problem to show that it's not a NP problem.
-----Input-----
The first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9).
-----Output-----
Print single integer, the integer that appears maximum number of times in the divisors.
If there are multiple answers, print any of them.
-----Examples-----
Input
19 29
Output
2
Input
3 6
Output
3
-----Note-----
Definition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html
The first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.
The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
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37\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "56 92\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "900000000 1000000000\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "37622224 162971117\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "760632746 850720703\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "908580370 968054552\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "951594860 953554446\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "347877978 913527175\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "620769961 988145114\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "820844234 892579936\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "741254764 741254768\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "80270976 80270977\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "392602363 392602367\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "519002744 519002744\n", "output": "519002744\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "331900277 331900277\n", "output": "331900277\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "419873015 419873018\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "349533413 349533413\n", "output": "349533413\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "28829775 28829776\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "568814539 568814539\n", "output": "568814539\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "720270740 720270743\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "871232720 871232722\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "305693653 305693653\n", "output": "305693653\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "634097178 634097179\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "450868287 450868290\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "252662256 252662260\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "575062045 575062049\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "273072892 273072894\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "770439256 770439256\n", "output": "770439256\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1000000000\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6 8\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 879190747\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5 5\n", "output": "5\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999937 999999937\n", "output": "999999937\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5 100\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 2\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 18\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7 7\n", "output": "7\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "39916801 39916801\n", "output": "39916801\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 8\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "13 13\n", "output": "13\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 8\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 12\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6 12\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999103 999999103\n", "output": "999999103\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "100000007 100000007\n", "output": "100000007\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 99\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999733 999999733\n", "output": "999999733\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5 10\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "982451653 982451653\n", "output": "982451653\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999900001 1000000000\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999727999 999727999\n", "output": "999727999\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 999999999\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "242 244\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 10\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15 27\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "998244353 998244353\n", "output": "998244353\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5 15\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999797 999999797\n", "output": "999999797\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 3\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999929 999999929\n", "output": "999999929\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 111111\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "12 18\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "479001599 479001599\n", "output": "479001599\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000019 10000019\n", "output": "10000019\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "715827883 715827883\n", "output": "715827883\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999992977 999992977\n", "output": "999992977\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11 11\n", "output": "11\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "29 29\n", "output": "29\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000003 1000003\n", "output": "1000003\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6 15\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1200007 1200007\n", "output": "1200007\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 1000000000\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "990000023 990000023\n", "output": "990000023\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1717 1717\n", "output": "1717\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "141650963 141650963\n", "output": "141650963\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1002523 1002523\n", "output": "1002523\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "900000011 900000011\n", "output": "900000011\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "104729 104729\n", "output": "104729\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 12\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "100003 100003\n", "output": "100003\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "17 17\n", "output": "17\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 100\n", "output": "2\n", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_2
| 2
|
[
{
"answer": "(a, b) = map(int, input().split())\nprint(2 if a != b else a)\n",
"question": "Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.\n\nYou are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.\n\nSolve the problem to show that it's not a NP problem.\n\n\n-----Input-----\n\nThe first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9).\n\n\n-----Output-----\n\nPrint single integer, the integer that appears maximum number of times in the divisors. \n\nIf there are multiple answers, print any of them.\n\n\n-----Examples-----\nInput\n19 29\n\nOutput\n2\n\nInput\n3 6\n\nOutput\n3\n\n\n\n-----Note-----\n\nDefinition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html\n\nThe first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.\n\nThe second example: from 3 to 6 these numbers are divisible by 3: {3, 6}."
},
{
"answer": "```python\nl,r=map(int,input().split())\nprint('YES')\nfor i in range((r-l+1)//2):\n print(l+i*2,l+i*2+1)\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nYou are given a set of all integers from l to r inclusive, l < r, (r - l + 1) ≤ 3 ⋅ 10^5 and (r - l) is always odd.\n\nYou want to split these numbers into exactly (r - l + 1)/(2) pairs in such a way that for each pair (i, j) the greatest common divisor of i and j is equal to 1. Each number should appear in exactly one of the pairs.\n\nPrint the resulting pairs or output that no solution exists. If there are multiple solutions, print any of them.\n\nInput\n\nThe only line contains two integers l and r (1 ≤ l < r ≤ 10^{18}, r - l + 1 ≤ 3 ⋅ 10^5, (r - l) is odd).\n\nOutput\n\nIf any solution exists, print \"YES\" in the first line. Each of the next (r - l + 1)/(2) lines should contain some pair of integers. GCD of numbers in each pair should be equal to 1. All (r - l + 1) numbers should be pairwise distinct and should have values from l to r inclusive.\n\nIf there are multiple solutions, print any of them.\n\nIf there exists no solution, print \"NO\".\n\nExample\n\nInput\n\n1 8\n\n\nOutput\n\nYES\n2 7\n4 1\n3 8\n6 5\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "```python\nT = int(input())\nfor ks in range(T):\n\t(l, r) = map(int, input().split())\n\tprint(l, 2 * l)\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nYou are given a range of positive integers from $l$ to $r$.\n\nFind such a pair of integers $(x, y)$ that $l \\le x, y \\le r$, $x \\ne y$ and $x$ divides $y$.\n\nIf there are multiple answers, print any of them.\n\nYou are also asked to answer $T$ independent queries.\n\n\n-----Input-----\n\nThe first line contains a single integer $T$ ($1 \\le T \\le 1000$) — the number of queries.\n\nEach of the next $T$ lines contains two integers $l$ and $r$ ($1 \\le l \\le r \\le 998244353$) — inclusive borders of the range.\n\nIt is guaranteed that testset only includes queries, which have at least one suitable pair.\n\n\n-----Output-----\n\nPrint $T$ lines, each line should contain the answer — two integers $x$ and $y$ such that $l \\le x, y \\le r$, $x \\ne y$ and $x$ divides $y$. The answer in the $i$-th line should correspond to the $i$-th query from the input.\n\nIf there are multiple answers, print any of them.\n\n\n-----Example-----\nInput\n3\n1 10\n3 14\n1 10\n\nOutput\n1 7\n3 9\n5 10\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
}
] |
Solve the following coding problem using the programming language python:
"QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth.
Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu
Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact.
-----Input-----
The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.
-----Output-----
Print a single integer — the number of subsequences "QAQ" in the string.
-----Examples-----
Input
QAQAQYSYIOIWIN
Output
4
Input
QAQQQZZYNOIWIN
Output
3
-----Note-----
In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN".
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\ns=input()\nans = 0\nfor i in range(len(s)):\n if s[i] == 'A':\n ans += s[:i].count('Q') * s[i:].count('Q')\nprint(ans)\n```"
] |
[{"type": "stdin_stdout", "input": "QAQAQYSYIOIWIN\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "QAQQQZZYNOIWIN\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "QA\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "IAQVAQZLQBQVQFTQQQADAQJA\n", "output": "24\n"}, {"type": "stdin_stdout", "input": "QQAAQASGAYAAAAKAKAQIQEAQAIAAIAQQQQQ\n", "output": "378\n"}, {"type": "stdin_stdout", "input": "AMVFNFJIAVNQJWIVONQOAOOQSNQSONOASONAONQINAONAOIQONANOIQOANOQINAONOQINAONOXJCOIAQOAOQAQAQAQAQWWWAQQAQ\n", "output": "1077\n"}, {"type": "stdin_stdout", "input": "AAQQAXBQQBQQXBNQRJAQKQNAQNQVDQASAGGANQQQQTJFFQQQTQQA\n", "output": "568\n"}, {"type": "stdin_stdout", "input": "KAZXAVLPJQBQVQQQQQAPAQQGQTQVZQAAAOYA\n", "output": "70\n"}, {"type": "stdin_stdout", "input": "W\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "DBA\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "RQAWNACASAAKAGAAAAQ\n", "output": "10\n"}, {"type": "stdin_stdout", "input": "QJAWZAAOAAGIAAAAAOQATASQAEAAAAQFQQHPA\n", "output": "111\n"}, {"type": "stdin_stdout", "input": "QQKWQAQAAAAAAAAGAAVAQUEQQUMQMAQQQNQLAMAAAUAEAAEMAAA\n", "output": "411\n"}, {"type": "stdin_stdout", "input": "QQUMQAYAUAAGWAAAQSDAVAAQAAAASKQJJQQQQMAWAYYAAAAAAEAJAXWQQ\n", "output": "625\n"}, {"type": "stdin_stdout", "input": "QORZOYAQ\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "QCQAQAGAWAQQQAQAVQAQQQQAQAQQQAQAAATQAAVAAAQQQQAAAUUQAQQNQQWQQWAQAAQQKQYAQAAQQQAAQRAQQQWBQQQQAPBAQGQA\n", "output": "13174\n"}, {"type": "stdin_stdout", "input": "QQAQQAKQFAQLQAAWAMQAZQAJQAAQQOACQQAAAYANAQAQQAQAAQQAOBQQJQAQAQAQQQAAAAABQQQAVNZAQQQQAMQQAFAAEAQAQHQT\n", "output": "10420\n"}, {"type": "stdin_stdout", "input": "AQEGQHQQKQAQQPQKAQQQAAAAQQQAQEQAAQAAQAQFSLAAQQAQOQQAVQAAAPQQAWAQAQAFQAXAQQQQTRLOQAQQJQNQXQQQQSQVDQQQ\n", "output": "12488\n"}, {"type": "stdin_stdout", "input": "QNQKQQQLASQBAVQQQQAAQQOQRJQQAQQQEQZUOANAADAAQQJAQAQARAAAQQQEQBHTQAAQAAAAQQMKQQQIAOJJQQAQAAADADQUQQQA\n", "output": "9114\n"}, {"type": "stdin_stdout", "input": "QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ\n", "output": "35937\n"}, {"type": "stdin_stdout", "input": "AMQQAAQAAQAAAAAAQQQBOAAANAAKQJCYQAE\n", "output": "254\n"}, {"type": "stdin_stdout", "input": "AYQBAEQGAQEOAKGIXLQJAIAKQAAAQPUAJAKAATFWQQAOQQQUFQYAQQMQHOKAAJXGFCARAQSATHAUQQAATQJJQDQRAANQQAE\n", "output": "2174\n"}, {"type": "stdin_stdout", "input": "AAQXAAQAYQAAAAGAQHVQYAGIVACADFAAQAAAAQZAAQMAKZAADQAQDAAQDAAAMQQOXYAQQQAKQBAAQQKAXQBJZDDLAAHQQ\n", "output": "2962\n"}, {"type": "stdin_stdout", "input": "AYQQYAVAMNIAUAAKBBQVACWKTQSAQZAAQAAASZJAWBCAALAARHACQAKQQAQAARPAQAAQAQAAZQUSHQAMFVFZQQQQSAQQXAA\n", "output": "2482\n"}, {"type": "stdin_stdout", "input": "LQMAQQARQAQBJQQQAGAAZQQXALQQAARQAQQQQAAQQAQQQAQQCAQQAQQAYQQQRAAZATQALYQQAAHHAAQHAAAAAAAAQQMAAQNAKQ\n", "output": "7768\n"}, {"type": "stdin_stdout", "input": "MAQQWAQOYQMAAAQAQPQZAOAAQAUAQNAAQAAAITQSAQAKAQKAQQWSQAAQQAGUCDQMQWKQUXKWQQAAQQAAQQZQDQQQAABXQUUXQOA\n", "output": "5422\n"}, {"type": "stdin_stdout", "input": "QTAAQDAQXAQQJQQQGAAAQQQQSBQZKAQQAQQQQEAQNUQBZCQLYQZQEQQAAQHQVAORKQVAQYQNASZQAARZAAGAAAAOQDCQ\n", "output": "3024\n"}, {"type": "stdin_stdout", "input": "QQWAQQGQQUZQQQLZAAQYQXQVAQFQUAQZUQZZQUKBHSHTQYLQAOQXAQQGAQQTQOAQARQADAJRAAQPQAQQUQAUAMAUVQAAAQQAWQ\n", "output": "4527\n"}, {"type": "stdin_stdout", "input": "QQAAQQAQVAQZQQQQAOEAQZPQIBQZACQQAFQQLAAQDATZQANHKYQQAQTAAFQRQAIQAJPWQAQTEIRXAEQQAYWAAAUKQQAQAQQQSQQH\n", "output": "6416\n"}, {"type": "stdin_stdout", "input": "AQQQQAQAAQQAQAQAAAAAAAAAQAQAAAAAQAQAQQQAQQQAAAQQQAAAAAAAQAAAAQQQQQQQAQQQQAQAAAQAAAAAQAQAAAAAQAQAAAA\n", "output": "14270\n"}, {"type": "stdin_stdout", "input": "AQQQQAQAAQQAQAQAAAAAAAAAQAQAAAAAQAQAQQQAQQQAAAQQQAAAAAAAQAAAAQQQQQQQAQQQQAQAAAQAAAAAQAQAAAAAQ\n", "output": "13136\n"}, {"type": "stdin_stdout", "input": "AQQQQAQAAQQAQAQAAAAAAAAAQAQAAAAAQAQAQQQAQQQAAAQQQAAAAAAAQAAAAQQQQQQQAQQQQAQAAAQAAAAAQAQAAAAAQAQAA\n", "output": "14270\n"}, {"type": "stdin_stdout", "input": "AQQQQAQAAQQAQAQAAAAAAAAAQAQAAAAAQAQAQQQAQQQAAAQQQAAAAAAAQAAAAQQQQQQQAQQQQAQAAAQAAAAAQAQAAAAAQQAA\n", "output": "14231\n"}, {"type": "stdin_stdout", "input": "QQQQQAQAAQQAQAQAAAAAAAAAQAQAAAAAQAQAQQQAQQQAAAQQQAAAAAAAQAAAAQQQQQQQAQQQQAQAAAQAAAAAQAQAAAAAQAQAA\n", "output": "15296\n"}, {"type": "stdin_stdout", "input": "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "QAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQA\n", "output": "20825\n"}, {"type": "stdin_stdout", "input": "AQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQ\n", "output": "20825\n"}, {"type": "stdin_stdout", "input": "Q\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "A\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "FFF\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "AAAAAA\n", "output": "0\n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
"QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth.
Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu
Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact.
-----Input-----
The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.
-----Output-----
Print a single integer — the number of subsequences "QAQ" in the string.
-----Examples-----
Input
QAQAQYSYIOIWIN
Output
4
Input
QAQQQZZYNOIWIN
Output
3
-----Note-----
In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN".
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
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{"func_name": null}}, {"type": "stdin_stdout", "input": "W\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "DBA\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "RQAWNACASAAKAGAAAAQ\n", "output": "10\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QJAWZAAOAAGIAAAAAOQATASQAEAAAAQFQQHPA\n", "output": "111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QQKWQAQAAAAAAAAGAAVAQUEQQUMQMAQQQNQLAMAAAUAEAAEMAAA\n", "output": "411\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QQUMQAYAUAAGWAAAQSDAVAAQAAAASKQJJQQQQMAWAYYAAAAAAEAJAXWQQ\n", "output": "625\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QORZOYAQ\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QCQAQAGAWAQQQAQAVQAQQQQAQAQQQAQAAATQAAVAAAQQQQAAAUUQAQQNQQWQQWAQAAQQKQYAQAAQQQAAQRAQQQWBQQQQAPBAQGQA\n", "output": 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|
livecodebench
|
deepcoder_3
| 3
|
[
{
"answer": "```python\n# QAQ\ndef crying(s):\n ans = 0\n for i in range(len(s)):\n if (s[i] != \"Q\"):\n continue\n for j in range(i + 1, len(s)):\n if s[j] != 'A':\n continue\n for k in range(j + 1, len(s)):\n if s[k] == 'Q':\n ans += 1\n \n\n return ans\n\n\n\n\ns = input()\nprint(crying(s))\n```",
"question": "Solve the following coding problem using the programming language python:\n\n\"QAQ\" is a word to denote an expression of crying. Imagine \"Q\" as eyes with tears and \"A\" as a mouth.\n\nNow Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of \"QAQ\" in the string (Diamond is so cute!).\n\n<image> illustration by 猫屋 https://twitter.com/nekoyaliu\n\nBort wants to know how many subsequences \"QAQ\" are in the string Diamond has given. Note that the letters \"QAQ\" don't have to be consecutive, but the order of letters should be exact.\n\nInput\n\nThe only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.\n\nOutput\n\nPrint a single integer — the number of subsequences \"QAQ\" in the string.\n\nExamples\n\nInput\n\nQAQAQYSYIOIWIN\n\n\nOutput\n\n4\n\n\nInput\n\nQAQQQZZYNOIWIN\n\n\nOutput\n\n3\n\nNote\n\nIn the first example there are 4 subsequences \"QAQ\": \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\".\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "import sys\nimport math\nimport bisect\n\ndef main():\n\ts = input()\n\tn = len(s)\n\tans = 0\n\tfor i in range(n):\n\t\tfor j in range(i + 1, n):\n\t\t\tfor k in range(j + 1, n):\n\t\t\t\tif s[i] + s[j] + s[k] == 'QAQ':\n\t\t\t\t\tans += 1\n\tprint(ans)\nmain()\n",
"question": "\"QAQ\" is a word to denote an expression of crying. Imagine \"Q\" as eyes with tears and \"A\" as a mouth.\n\nNow Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of \"QAQ\" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu \n\nBort wants to know how many subsequences \"QAQ\" are in the string Diamond has given. Note that the letters \"QAQ\" don't have to be consecutive, but the order of letters should be exact.\n\n\n-----Input-----\n\nThe only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.\n\n\n-----Output-----\n\nPrint a single integer — the number of subsequences \"QAQ\" in the string.\n\n\n-----Examples-----\nInput\nQAQAQYSYIOIWIN\n\nOutput\n4\n\nInput\nQAQQQZZYNOIWIN\n\nOutput\n3\n\n\n\n-----Note-----\n\nIn the first example there are 4 subsequences \"QAQ\": \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\"."
},
{
"answer": "```python\nimport sys\n\ninput = sys.stdin.readline\n\nn, q = map(int, input().split())\ns, psa = [ord(char) - 96 for char in input().strip()], [0]\nfor i in range(n):\n psa.append(s[i] + psa[i])\n\nfor _ in range(q):\n l, r = map(int, input().split())\n print(psa[r] - psa[l - 1])\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nPetya once wrote a sad love song and shared it to Vasya. The song is a string consisting of lowercase English letters. Vasya made up q questions about this song. Each question is about a subsegment of the song starting from the l-th letter to the r-th letter. Vasya considers a substring made up from characters on this segment and repeats each letter in the subsegment k times, where k is the index of the corresponding letter in the alphabet. For example, if the question is about the substring \"abbcb\", then Vasya repeats letter 'a' once, each of the letters 'b' twice, letter 'c\" three times, so that the resulting string is \"abbbbcccbb\", its length is 10. Vasya is interested about the length of the resulting string.\n\nHelp Petya find the length of each string obtained by Vasya.\n\nInput\n\nThe first line contains two integers n and q (1≤ n≤ 100 000, 1≤ q ≤ 100 000) — the length of the song and the number of questions. \n\nThe second line contains one string s — the song, consisting of n lowercase letters of English letters.\n\nVasya's questions are contained in the next q lines. Each line contains two integers l and r (1 ≤ l ≤ r ≤ n) — the bounds of the question.\n\nOutput\n\nPrint q lines: for each question print the length of the string obtained by Vasya.\n\nExamples\n\nInput\n\n\n7 3\nabacaba\n1 3\n2 5\n1 7\n\n\nOutput\n\n\n4\n7\n11\n\n\nInput\n\n\n7 4\nabbabaa\n1 3\n5 7\n6 6\n2 4\n\n\nOutput\n\n\n5\n4\n1\n5\n\n\nInput\n\n\n13 7\nsonoshikumiwo\n1 5\n2 10\n7 7\n1 13\n4 8\n2 5\n3 9\n\n\nOutput\n\n\n82\n125\n9\n191\n62\n63\n97\n\nNote\n\nIn the first example Vasya is interested in three questions. In the first question Vasya considers the substring \"aba\", that transforms to \"abba\", so the answer is equal to 4. In the second question Vasya considers \"baca\", that transforms to \"bbaccca\", so the answer is 7. In the third question Vasya considers the string \"abacaba\",that transforms to \"abbacccabba\" of length 11.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
}
] |
Solve the following coding problem using the programming language python:
Codefortia is a small island country located somewhere in the West Pacific. It consists of $n$ settlements connected by $m$ bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to $a$ or $b$ seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads.
Codefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that:
it will be possible to travel between each pair of cities using the remaining roads only, the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement $1$) and the parliament house (in settlement $p$) using the remaining roads only will be minimum possible.
The king, however, forgot where the parliament house was. For each settlement $p = 1, 2, \dots, n$, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement $p$) after some roads are abandoned?
-----Input-----
The first line of the input contains four integers $n$, $m$, $a$ and $b$ ($2 \leq n \leq 70$, $n - 1 \leq m \leq 200$, $1 \leq a < b \leq 10^7$) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers $u, v, c$ ($1 \leq u, v \leq n$, $u \neq v$, $c \in \{a, b\}$) denoting a single gravel road between the settlements $u$ and $v$, which requires $c$ minutes to travel.
You can assume that the road network is connected and has no loops or multiedges.
-----Output-----
Output a single line containing $n$ integers. The $p$-th of them should denote the minimum possible time required to travel from $1$ to $p$ after the selected roads are abandoned. Note that for each $p$ you can abandon a different set of roads.
-----Examples-----
Input
5 5 20 25
1 2 25
2 3 25
3 4 20
4 5 20
5 1 20
Output
0 25 60 40 20
Input
6 7 13 22
1 2 13
2 3 13
1 4 22
3 4 13
4 5 13
5 6 13
6 1 13
Output
0 13 26 39 26 13
-----Note-----
The minimum possible sum of times required to pass each road in the first example is $85$ — exactly one of the roads with passing time $25$ must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements $1$ and $3$ in time $50$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\nimport heapq\nn,m,a,b=map(int,input().split())\ngraph={i:[] for i in range(n)}\nfor i in range(m):\n u,v,w=map(int,input().split())\n graph[u-1].append((v-1,w))\n graph[v-1].append((u-1,w))\ncomponents=[-1]*n\ncomp=-1\nfor i in range(n):\n if components[i]==-1:\n comp+=1\n components[i]=comp\n prev=[]\n layer=[i]\n while layer!=[]:\n newlayer=[]\n for guy in layer:\n for guy1 in graph[guy]:\n if guy1[1]==a and components[guy1[0]]==-1:\n newlayer.append(guy1[0])\n components[guy1[0]]=comp\n prev=layer[:]\n layer=newlayer[:]\nuseless=[]\nfor guy in graph:\n for neigh in graph[guy]:\n if components[guy]==components[neigh[0]] and neigh[1]==b:\n useless.append((guy,neigh))\nfor guy in useless:\n graph[guy[0]].remove(guy[1])\ncounts=[0]*(comp+1)\nfor i in range(n):\n counts[components[i]]+=1\nbad=[]\nfor i in range(comp+1):\n if counts[i]<=3:\n bad.append(i)\n for j in range(n):\n if components[j]==i:\n components[j]=-1\nfor guy in bad[::-1]:\n for i in range(n):\n if components[i]>guy:\n components[i]-=1\ncomp-=len(bad)\ncomp+=1\ndists=[[float(\"inf\") for i in range(2**comp)] for j in range(n)]\ndists[0][0]=0\npq=[]\nheapq.heappush(pq,[0,0,0])\nremaining=n\nvisited=[0]*n\nwhile len(pq)>0 and remaining>0:\n dist,vert,mask=heapq.heappop(pq)\n if visited[vert]==0:\n visited[vert]=1\n remaining-=1\n for neigh in graph[vert]:\n if neigh[1]==b:\n if components[vert]==components[neigh[0]] and components[vert]!=-1:\n continue\n if components[neigh[0]]!=-1:\n if mask & (2**components[neigh[0]])>0:\n continue\n if components[vert]!=-1:\n maskn=mask+2**(components[vert])\n else:\n maskn=mask\n else:\n maskn=mask\n if dist+neigh[1]<dists[neigh[0]][maskn]:\n dists[neigh[0]][maskn]=dist+neigh[1]\n heapq.heappush(pq,[dist+neigh[1],neigh[0],maskn])\noptimal=[str(min(dists[i])) for i in range(n)]\nprint(\" \".join(optimal))\n```"
] |
[{"type": "stdin_stdout", "input": "5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n", "output": "0 25 60 40 20\n"}, {"type": "stdin_stdout", "input": "6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n", "output": "0 13 26 39 26 13\n"}, {"type": "stdin_stdout", "input": "2 1 1 2\n2 1 1\n", "output": "0 1\n"}, {"type": "stdin_stdout", "input": "2 1 9999999 10000000\n1 2 10000000\n", "output": "0 10000000\n"}, {"type": "stdin_stdout", "input": "3 3 78422 6789101\n3 1 6789101\n2 1 78422\n2 3 78422\n", "output": "0 78422 156844\n"}, {"type": "stdin_stdout", "input": "3 3 2770628 3912422\n1 2 2770628\n2 3 2770628\n1 3 3912422\n", "output": "0 2770628 5541256\n"}, {"type": "stdin_stdout", "input": "3 3 2566490 5132980\n1 2 2566490\n2 3 2566490\n3 1 5132980\n", "output": "0 2566490 5132980\n"}, {"type": "stdin_stdout", "input": "3 2 509529 5982470\n1 2 509529\n3 2 509529\n", "output": "0 509529 1019058\n"}, {"type": "stdin_stdout", "input": "3 2 1349740 8457492\n2 1 1349740\n3 1 1349740\n", "output": "0 1349740 1349740\n"}, {"type": "stdin_stdout", "input": "3 2 150319 5002968\n3 2 150319\n1 2 5002968\n", "output": "0 5002968 5153287\n"}, {"type": "stdin_stdout", "input": "3 2 990530 8623767\n3 2 8623767\n1 2 990530\n", "output": "0 990530 9614297\n"}, {"type": "stdin_stdout", "input": "3 2 810925 2022506\n1 2 2022506\n1 3 810925\n", "output": "0 2022506 810925\n"}, {"type": "stdin_stdout", "input": "3 2 1651136 5131013\n1 2 5131013\n3 2 5131013\n", "output": "0 5131013 10262026\n"}, {"type": "stdin_stdout", "input": "3 2 451715 1577270\n1 3 1577270\n1 2 1577270\n", "output": "0 1577270 1577270\n"}, {"type": "stdin_stdout", "input": "3 3 1291926 4943478\n2 3 1291926\n1 2 1291926\n3 1 1291926\n", "output": "0 1291926 1291926\n"}, {"type": "stdin_stdout", "input": "3 3 2132137 9084127\n1 2 2132137\n3 2 9084127\n3 1 2132137\n", "output": "0 2132137 2132137\n"}, {"type": "stdin_stdout", "input": "3 3 1126640 9858678\n3 1 9858678\n3 2 1126640\n1 2 9858678\n", "output": "0 9858678 9858678\n"}, {"type": "stdin_stdout", "input": "3 3 1966851 6439891\n1 3 6439891\n1 2 1966851\n3 2 6439891\n", "output": "0 1966851 6439891\n"}, {"type": "stdin_stdout", "input": "3 3 1787246 7806211\n3 2 7806211\n2 1 7806211\n1 3 7806211\n", "output": "0 7806211 7806211\n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
Codefortia is a small island country located somewhere in the West Pacific. It consists of $n$ settlements connected by $m$ bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to $a$ or $b$ seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads.
Codefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that:
it will be possible to travel between each pair of cities using the remaining roads only, the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement $1$) and the parliament house (in settlement $p$) using the remaining roads only will be minimum possible.
The king, however, forgot where the parliament house was. For each settlement $p = 1, 2, \dots, n$, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement $p$) after some roads are abandoned?
-----Input-----
The first line of the input contains four integers $n$, $m$, $a$ and $b$ ($2 \leq n \leq 70$, $n - 1 \leq m \leq 200$, $1 \leq a < b \leq 10^7$) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers $u, v, c$ ($1 \leq u, v \leq n$, $u \neq v$, $c \in \{a, b\}$) denoting a single gravel road between the settlements $u$ and $v$, which requires $c$ minutes to travel.
You can assume that the road network is connected and has no loops or multiedges.
-----Output-----
Output a single line containing $n$ integers. The $p$-th of them should denote the minimum possible time required to travel from $1$ to $p$ after the selected roads are abandoned. Note that for each $p$ you can abandon a different set of roads.
-----Examples-----
Input
5 5 20 25
1 2 25
2 3 25
3 4 20
4 5 20
5 1 20
Output
0 25 60 40 20
Input
6 7 13 22
1 2 13
2 3 13
1 4 22
3 4 13
4 5 13
5 6 13
6 1 13
Output
0 13 26 39 26 13
-----Note-----
The minimum possible sum of times required to pass each road in the first example is $85$ — exactly one of the roads with passing time $25$ must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements $1$ and $3$ in time $50$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
[{"type": "stdin_stdout", "input": "5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n", "output": "0 25 60 40 20\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n", "output": "0 13 26 39 26 13\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1 1 2\n2 1 1\n", "output": "0 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1 9999999 10000000\n1 2 10000000\n", "output": "0 10000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 78422 6789101\n3 1 6789101\n2 1 78422\n2 3 78422\n", "output": "0 78422 156844\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2770628 3912422\n1 2 2770628\n2 3 2770628\n1 3 3912422\n", "output": "0 2770628 5541256\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2566490 5132980\n1 2 2566490\n2 3 2566490\n3 1 5132980\n", "output": "0 2566490 5132980\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 509529 5982470\n1 2 509529\n3 2 509529\n", "output": "0 509529 1019058\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 1349740 8457492\n2 1 1349740\n3 1 1349740\n", "output": "0 1349740 1349740\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 150319 5002968\n3 2 150319\n1 2 5002968\n", "output": "0 5002968 5153287\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 990530 8623767\n3 2 8623767\n1 2 990530\n", "output": "0 990530 9614297\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 810925 2022506\n1 2 2022506\n1 3 810925\n", "output": "0 2022506 810925\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 1651136 5131013\n1 2 5131013\n3 2 5131013\n", "output": "0 5131013 10262026\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 451715 1577270\n1 3 1577270\n1 2 1577270\n", "output": "0 1577270 1577270\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1291926 4943478\n2 3 1291926\n1 2 1291926\n3 1 1291926\n", "output": "0 1291926 1291926\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2132137 9084127\n1 2 2132137\n3 2 9084127\n3 1 2132137\n", "output": "0 2132137 2132137\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1126640 9858678\n3 1 9858678\n3 2 1126640\n1 2 9858678\n", "output": "0 9858678 9858678\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1966851 6439891\n1 3 6439891\n1 2 1966851\n3 2 6439891\n", "output": "0 1966851 6439891\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1787246 7806211\n3 2 7806211\n2 1 7806211\n1 3 7806211\n", "output": "0 7806211 7806211\n", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_4
| 4
|
[
{
"answer": "```python\nimport heapq\nn,m,a,b=map(int,input().split())\ngraph={i:[] for i in range(n)}\nfor i in range(m):\n u,v,w=map(int,input().split())\n graph[u-1].append((v-1,w))\n graph[v-1].append((u-1,w))\ncomponents=[-1]*n\ncomp=-1\nfor i in range(n):\n if components[i]==-1:\n comp+=1\n components[i]=comp\n prev=[]\n layer=[i]\n while layer!=[]:\n newlayer=[]\n for guy in layer:\n for guy1 in graph[guy]:\n if guy1[1]==a and components[guy1[0]]==-1:\n newlayer.append(guy1[0])\n components[guy1[0]]=comp\n prev=layer[:]\n layer=newlayer[:]\nuseless=[]\nfor guy in graph:\n for neigh in graph[guy]:\n if components[guy]==components[neigh[0]] and neigh[1]==b:\n useless.append((guy,neigh))\nfor guy in useless:\n graph[guy[0]].remove(guy[1])\ncounts=[0]*(comp+1)\nfor i in range(n):\n counts[components[i]]+=1\nbad=[]\nfor i in range(comp+1):\n if counts[i]<=3:\n bad.append(i)\n for j in range(n):\n if components[j]==i:\n components[j]=-1\nfor guy in bad[::-1]:\n for i in range(n):\n if components[i]>guy:\n components[i]-=1\ncomp-=len(bad)\ncomp+=1\ndists=[[float(\"inf\") for i in range(2**comp)] for j in range(n)]\ndists[0][0]=0\npq=[]\nheapq.heappush(pq,[0,0,0])\nremaining=n\nvisited=[0]*n\nwhile len(pq)>0 and remaining>0:\n dist,vert,mask=heapq.heappop(pq)\n if visited[vert]==0:\n visited[vert]=1\n remaining-=1\n for neigh in graph[vert]:\n if neigh[1]==b:\n if components[vert]==components[neigh[0]] and components[vert]!=-1:\n continue\n if components[neigh[0]]!=-1:\n if mask & (2**components[neigh[0]])>0:\n continue\n if components[vert]!=-1:\n maskn=mask+2**(components[vert])\n else:\n maskn=mask\n else:\n maskn=mask\n if dist+neigh[1]<dists[neigh[0]][maskn]:\n dists[neigh[0]][maskn]=dist+neigh[1]\n heapq.heappush(pq,[dist+neigh[1],neigh[0],maskn])\noptimal=[str(min(dists[i])) for i in range(n)]\nprint(\" \".join(optimal))\n```",
"question": "Solve the following coding problem using the programming language python:\n\nCodefortia is a small island country located somewhere in the West Pacific. It consists of n settlements connected by m bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to a or b seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads.\n\nCodefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that:\n\n * it will be possible to travel between each pair of cities using the remaining roads only, \n * the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), \n * among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement 1) and the parliament house (in settlement p) using the remaining roads only will be minimum possible. \n\n\n\nThe king, however, forgot where the parliament house was. For each settlement p = 1, 2, ..., n, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement p) after some roads are abandoned?\n\nInput\n\nThe first line of the input contains four integers n, m, a and b (2 ≤ n ≤ 70, n - 1 ≤ m ≤ 200, 1 ≤ a < b ≤ 10^7) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers u, v, c (1 ≤ u, v ≤ n, u ≠ v, c ∈ \\\\{a, b\\}) denoting a single gravel road between the settlements u and v, which requires c minutes to travel.\n\nYou can assume that the road network is connected and has no loops or multiedges.\n\nOutput\n\nOutput a single line containing n integers. The p-th of them should denote the minimum possible time required to travel from 1 to p after the selected roads are abandoned. Note that for each p you can abandon a different set of roads.\n\nExamples\n\nInput\n\n\n5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n\n\nOutput\n\n\n0 25 60 40 20\n\n\nInput\n\n\n6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n\n\nOutput\n\n\n0 13 26 39 26 13\n\nNote\n\nThe minimum possible sum of times required to pass each road in the first example is 85 — exactly one of the roads with passing time 25 must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements 1 and 3 in time 50.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "import heapq\n(n, m, a, b) = map(int, input().split())\ngraph = {i: [] for i in range(n)}\nfor i in range(m):\n\t(u, v, w) = map(int, input().split())\n\tgraph[u - 1].append((v - 1, w))\n\tgraph[v - 1].append((u - 1, w))\ncomponents = [-1] * n\ncomp = -1\nfor i in range(n):\n\tif components[i] == -1:\n\t\tcomp += 1\n\t\tcomponents[i] = comp\n\t\tprev = []\n\t\tlayer = [i]\n\t\twhile layer != []:\n\t\t\tnewlayer = []\n\t\t\tfor guy in layer:\n\t\t\t\tfor guy1 in graph[guy]:\n\t\t\t\t\tif guy1[1] == a and components[guy1[0]] == -1:\n\t\t\t\t\t\tnewlayer.append(guy1[0])\n\t\t\t\t\t\tcomponents[guy1[0]] = comp\n\t\t\tprev = layer[:]\n\t\t\tlayer = newlayer[:]\nuseless = []\nfor guy in graph:\n\tfor neigh in graph[guy]:\n\t\tif components[guy] == components[neigh[0]] and neigh[1] == b:\n\t\t\tuseless.append((guy, neigh))\nfor guy in useless:\n\tgraph[guy[0]].remove(guy[1])\ncounts = [0] * (comp + 1)\nfor i in range(n):\n\tcounts[components[i]] += 1\nbad = []\nfor i in range(comp + 1):\n\tif counts[i] <= 3:\n\t\tbad.append(i)\n\t\tfor j in range(n):\n\t\t\tif components[j] == i:\n\t\t\t\tcomponents[j] = -1\nfor guy in bad[::-1]:\n\tfor i in range(n):\n\t\tif components[i] > guy:\n\t\t\tcomponents[i] -= 1\ncomp -= len(bad)\ncomp += 1\ndists = [[float('inf') for i in range(2 ** comp)] for j in range(n)]\ndists[0][0] = 0\npq = []\nheapq.heappush(pq, [0, 0, 0])\nremaining = n\nvisited = [0] * n\nwhile len(pq) > 0 and remaining > 0:\n\t(dist, vert, mask) = heapq.heappop(pq)\n\tif visited[vert] == 0:\n\t\tvisited[vert] = 1\n\t\tremaining -= 1\n\tfor neigh in graph[vert]:\n\t\tif neigh[1] == b:\n\t\t\tif components[vert] == components[neigh[0]] and components[vert] != -1:\n\t\t\t\tcontinue\n\t\t\tif components[neigh[0]] != -1:\n\t\t\t\tif mask & 2 ** components[neigh[0]] > 0:\n\t\t\t\t\tcontinue\n\t\t\tif components[vert] != -1:\n\t\t\t\tmaskn = mask + 2 ** components[vert]\n\t\t\telse:\n\t\t\t\tmaskn = mask\n\t\telse:\n\t\t\tmaskn = mask\n\t\tif dist + neigh[1] < dists[neigh[0]][maskn]:\n\t\t\tdists[neigh[0]][maskn] = dist + neigh[1]\n\t\t\theapq.heappush(pq, [dist + neigh[1], neigh[0], maskn])\noptimal = [str(min(dists[i])) for i in range(n)]\nprint(' '.join(optimal))\n",
"question": "Codefortia is a small island country located somewhere in the West Pacific. It consists of $n$ settlements connected by $m$ bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to $a$ or $b$ seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads.\n\nCodefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that:\n\n it will be possible to travel between each pair of cities using the remaining roads only, the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement $1$) and the parliament house (in settlement $p$) using the remaining roads only will be minimum possible. \n\nThe king, however, forgot where the parliament house was. For each settlement $p = 1, 2, \\dots, n$, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement $p$) after some roads are abandoned?\n\n\n-----Input-----\n\nThe first line of the input contains four integers $n$, $m$, $a$ and $b$ ($2 \\leq n \\leq 70$, $n - 1 \\leq m \\leq 200$, $1 \\leq a < b \\leq 10^7$) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers $u, v, c$ ($1 \\leq u, v \\leq n$, $u \\neq v$, $c \\in \\{a, b\\}$) denoting a single gravel road between the settlements $u$ and $v$, which requires $c$ minutes to travel.\n\nYou can assume that the road network is connected and has no loops or multiedges.\n\n\n-----Output-----\n\nOutput a single line containing $n$ integers. The $p$-th of them should denote the minimum possible time required to travel from $1$ to $p$ after the selected roads are abandoned. Note that for each $p$ you can abandon a different set of roads.\n\n\n-----Examples-----\nInput\n5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n\nOutput\n0 25 60 40 20\n\nInput\n6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n\nOutput\n0 13 26 39 26 13\n\n\n\n-----Note-----\n\nThe minimum possible sum of times required to pass each road in the first example is $85$ — exactly one of the roads with passing time $25$ must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements $1$ and $3$ in time $50$."
},
{
"answer": "```python\nn, m = list(map(int, input().split()))\ntable = [False] * (n + 1)\nfor _ in range(m):\n a, b = list(map(int, input().split()))\n table[a] = table[b] = True\nprint(n - 1)\nfor i in range(1, n + 1):\n if not table[i]:\n for j in range(1, n + 1):\n if i != j:\n print(i, j)\n break\n\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nA country has n cities. Initially, there is no road in the country. One day, the king decides to construct some roads connecting pairs of cities. Roads can be traversed either way. He wants those roads to be constructed in such a way that it is possible to go from each city to any other city by traversing at most two roads. You are also given m pairs of cities — roads cannot be constructed between these pairs of cities.\n\nYour task is to construct the minimum number of roads that still satisfy the above conditions. The constraints will guarantee that this is always possible.\n\n\n-----Input-----\n\nThe first line consists of two integers n and m $(1 \\leq n \\leq 10^{3}, 0 \\leq m < \\frac{n}{2})$.\n\nThen m lines follow, each consisting of two integers a_{i} and b_{i} (1 ≤ a_{i}, b_{i} ≤ n, a_{i} ≠ b_{i}), which means that it is not possible to construct a road connecting cities a_{i} and b_{i}. Consider the cities are numbered from 1 to n.\n\nIt is guaranteed that every pair of cities will appear at most once in the input.\n\n\n-----Output-----\n\nYou should print an integer s: the minimum number of roads that should be constructed, in the first line. Then s lines should follow, each consisting of two integers a_{i} and b_{i} (1 ≤ a_{i}, b_{i} ≤ n, a_{i} ≠ b_{i}), which means that a road should be constructed between cities a_{i} and b_{i}.\n\nIf there are several solutions, you may print any of them.\n\n\n-----Examples-----\nInput\n4 1\n1 3\n\nOutput\n3\n1 2\n4 2\n2 3\n\n\n\n-----Note-----\n\nThis is one possible solution of the example: [Image] \n\nThese are examples of wrong solutions: [Image] The above solution is wrong because it doesn't use the minimum number of edges (4 vs 3). In addition, it also tries to construct a road between cities 1 and 3, while the input specifies that it is not allowed to construct a road between the pair. [Image] The above solution is wrong because you need to traverse at least 3 roads to go from city 1 to city 3, whereas in your country it must be possible to go from any city to another by traversing at most 2 roads. [Image] Finally, the above solution is wrong because it must be possible to go from any city to another, whereas it is not possible in this country to go from city 1 to 3, 2 to 3, and 4 to 3.\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
}
] |
Solve the following coding problem using the programming language python:
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2^{n} - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 10^18.
Note the number of elements in the output array should not be more than 10^4. If no answer is possible, print - 1.
-----Input-----
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 10^9).
-----Output-----
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a_1, a_2, ... , a_{n} (1 ≤ a_{i} < 10^18).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
-----Examples-----
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
-----Note-----
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\nX, D = list(map(int, input().split()))\ncn = 1\nadd0 = 1 if (X&1) else 0\nans = []\nfor i in range(30,0,-1):\n\tif not (X & (1<<i)): continue\n\tans += [cn]*i\n\tadd0 += 1\n\tcn += D\nfor i in range(add0):\n\tans.append(cn)\n\tcn += D\nprint(len(ans))\nprint(' '.join(map(str, ans)))\n\n```"
] |
[{"type": "stdin_stdout", "input": "10 5\n", "output": "6\n1 1 1 7 13 19 "}, {"type": "stdin_stdout", "input": "4 2\n", "output": "3\n1 1 4 "}, {"type": "stdin_stdout", "input": "4 1\n", "output": "3\n1 1 3 "}, {"type": "stdin_stdout", "input": "1 1\n", "output": "1\n1 "}, {"type": "stdin_stdout", "input": "63 1\n", "output": "21\n1 1 1 1 1 3 3 3 3 5 5 5 7 7 9 11 13 15 17 19 21 "}, {"type": "stdin_stdout", "input": "98 88\n", "output": "15\n1 1 1 1 1 1 90 90 90 90 90 179 268 357 446 "}, {"type": "stdin_stdout", "input": "746 173\n", "output": "37\n1 1 1 1 1 1 1 1 1 175 175 175 175 175 175 175 349 349 349 349 349 349 523 523 523 523 523 697 697 697 871 1045 1219 1393 1567 1741 1915 "}, {"type": "stdin_stdout", "input": "890 553\n", "output": "43\n1 1 1 1 1 1 1 1 1 555 555 555 555 555 555 555 555 1109 1109 1109 1109 1109 1109 1663 1663 1663 1663 1663 2217 2217 2217 2217 2771 2771 2771 3325 3879 4433 4987 5541 6095 6649 7203 "}, {"type": "stdin_stdout", "input": "883 1000\n", "output": "40\n1 1 1 1 1 1 1 1 1 1002 1002 1002 1002 1002 1002 1002 1002 2003 2003 2003 2003 2003 2003 3004 3004 3004 3004 3004 4005 4005 4005 4005 5006 6007 7008 8009 9010 10011 11012 12013 "}, {"type": "stdin_stdout", "input": "1 1000\n", "output": "1\n1 "}, {"type": "stdin_stdout", "input": "695 188\n", "output": "35\n1 1 1 1 1 1 1 1 1 190 190 190 190 190 190 190 379 379 379 379 379 568 568 568 568 757 757 946 1135 1324 1513 1702 1891 2080 2269 "}, {"type": "stdin_stdout", "input": "2060 697\n", "output": "19\n1 1 1 1 1 1 1 1 1 1 1 699 699 699 1397 1397 2095 2793 3491 "}, {"type": "stdin_stdout", "input": "70 3321\n", "output": "12\n1 1 1 1 1 1 3323 3323 6645 9967 13289 16611 "}, {"type": "stdin_stdout", "input": "6358 1646\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 3295 3295 3295 3295 3295 3295 3295 4942 4942 4942 4942 4942 4942 6589 6589 6589 6589 8236 8236 9883 11530 13177 14824 16471 18118 19765 21412 "}, {"type": "stdin_stdout", "input": "15000 1\n", "output": "66\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 11 11 11 11 13 13 13 15 17 19 21 23 25 27 "}, {"type": "stdin_stdout", "input": "1048576 1\n", "output": "21\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 "}, {"type": "stdin_stdout", "input": "1000000 1\n", "output": "106\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 11 11 11 11 11 11 11 11 11 13 13 13 13 13 13 15 17 19 21 23 25 27 "}, {"type": "stdin_stdout", "input": "10009 1\n", "output": "54\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 11 11 13 15 17 19 21 23 25 "}, {"type": "stdin_stdout", "input": "10001 1\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 13 15 17 19 21 "}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2^{n} - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 10^18.
Note the number of elements in the output array should not be more than 10^4. If no answer is possible, print - 1.
-----Input-----
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 10^9).
-----Output-----
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a_1, a_2, ... , a_{n} (1 ≤ a_{i} < 10^18).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
-----Examples-----
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
-----Note-----
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
[{"type": "stdin_stdout", "input": "10 5\n", "output": "6\n1 1 1 7 13 19 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 2\n", "output": "3\n1 1 4 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 1\n", "output": "3\n1 1 3 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1\n", "output": "1\n1 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "63 1\n", "output": "21\n1 1 1 1 1 3 3 3 3 5 5 5 7 7 9 11 13 15 17 19 21 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "98 88\n", "output": "15\n1 1 1 1 1 1 90 90 90 90 90 179 268 357 446 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "746 173\n", "output": "37\n1 1 1 1 1 1 1 1 1 175 175 175 175 175 175 175 349 349 349 349 349 349 523 523 523 523 523 697 697 697 871 1045 1219 1393 1567 1741 1915 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "890 553\n", "output": "43\n1 1 1 1 1 1 1 1 1 555 555 555 555 555 555 555 555 1109 1109 1109 1109 1109 1109 1663 1663 1663 1663 1663 2217 2217 2217 2217 2771 2771 2771 3325 3879 4433 4987 5541 6095 6649 7203 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "883 1000\n", "output": "40\n1 1 1 1 1 1 1 1 1 1002 1002 1002 1002 1002 1002 1002 1002 2003 2003 2003 2003 2003 2003 3004 3004 3004 3004 3004 4005 4005 4005 4005 5006 6007 7008 8009 9010 10011 11012 12013 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1000\n", "output": "1\n1 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "695 188\n", "output": "35\n1 1 1 1 1 1 1 1 1 190 190 190 190 190 190 190 379 379 379 379 379 568 568 568 568 757 757 946 1135 1324 1513 1702 1891 2080 2269 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2060 697\n", "output": "19\n1 1 1 1 1 1 1 1 1 1 1 699 699 699 1397 1397 2095 2793 3491 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "70 3321\n", "output": "12\n1 1 1 1 1 1 3323 3323 6645 9967 13289 16611 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6358 1646\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 3295 3295 3295 3295 3295 3295 3295 4942 4942 4942 4942 4942 4942 6589 6589 6589 6589 8236 8236 9883 11530 13177 14824 16471 18118 19765 21412 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15000 1\n", "output": "66\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 11 11 11 11 13 13 13 15 17 19 21 23 25 27 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1048576 1\n", "output": "21\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000000 1\n", "output": "106\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 11 11 11 11 11 11 11 11 11 13 13 13 13 13 13 15 17 19 21 23 25 27 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10009 1\n", "output": "54\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 11 11 13 15 17 19 21 23 25 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10001 1\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 13 15 17 19 21 ", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_5
| 5
|
[
{
"answer": "```python\nX, d = map(int, input().split())\n\nx = X\nans = list()\nln = 0\nlast = 1\nwhile x > 0:\n if last >= 10 ** 18:\n print(-1)\n exit()\n\n i = 0\n while 2 ** (i + 1) - 1 <= x:\n i += 1\n\n t = 2 ** i - 1\n x -= t\n\n if ln + i > 10000:\n print(-1)\n exit()\n\n for _ in range(i):\n ans.append(last)\n ln += 1\n\n last += d\n\nprint(len(ans))\nprint(' '.join(map(str, ans)))\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nPikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it. \n\nPikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d\n\nPikachu was finally left with X subsequences. \n\nHowever, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018. \n\nNote the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.\n\nInput\n\nThe only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).\n\nOutput\n\nOutput should consist of two lines.\n\nFirst line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.\n\nSecond line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).\n\nIf there is no answer, print a single integer -1. If there are multiple answers, print any of them.\n\nExamples\n\nInput\n\n10 5\n\n\nOutput\n\n6\n5 50 7 15 6 100\n\nInput\n\n4 2\n\n\nOutput\n\n4\n10 100 1000 10000\n\nNote\n\nIn the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.\n\nSimilarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "```python\nfrom collections import *\ninput()\na = list(map(int, input().split()))\nm = defaultdict(int)\nfor x in reversed(a): m[x] = m[x + 1] + 1\nv = max(list(m.keys()), key=m.get)\nseq = []\nfor i, x in enumerate(a):\n if v == x:\n seq.append(i + 1)\n v += 1\nprint(len(seq))\nprint(*seq)\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nYou are given an integer array of length $n$.\n\nYou have to choose some subsequence of this array of maximum length such that this subsequence forms a increasing sequence of consecutive integers. In other words the required sequence should be equal to $[x, x + 1, \\dots, x + k - 1]$ for some value $x$ and length $k$.\n\nSubsequence of an array can be obtained by erasing some (possibly zero) elements from the array. You can erase any elements, not necessarily going successively. The remaining elements preserve their order. For example, for the array $[5, 3, 1, 2, 4]$ the following arrays are subsequences: $[3]$, $[5, 3, 1, 2, 4]$, $[5, 1, 4]$, but the array $[1, 3]$ is not.\n\n\n-----Input-----\n\nThe first line of the input containing integer number $n$ ($1 \\le n \\le 2 \\cdot 10^5$) — the length of the array. The second line of the input containing $n$ integer numbers $a_1, a_2, \\dots, a_n$ ($1 \\le a_i \\le 10^9$) — the array itself.\n\n\n-----Output-----\n\nOn the first line print $k$ — the maximum length of the subsequence of the given array that forms an increasing sequence of consecutive integers.\n\nOn the second line print the sequence of the indices of the any maximum length subsequence of the given array that forms an increasing sequence of consecutive integers.\n\n\n-----Examples-----\nInput\n7\n3 3 4 7 5 6 8\n\nOutput\n4\n2 3 5 6 \n\nInput\n6\n1 3 5 2 4 6\n\nOutput\n2\n1 4 \n\nInput\n4\n10 9 8 7\n\nOutput\n1\n1 \n\nInput\n9\n6 7 8 3 4 5 9 10 11\n\nOutput\n6\n1 2 3 7 8 9 \n\n\n\n-----Note-----\n\nAll valid answers for the first example (as sequences of indices): $[1, 3, 5, 6]$ $[2, 3, 5, 6]$ \n\nAll valid answers for the second example: $[1, 4]$ $[2, 5]$ $[3, 6]$ \n\nAll valid answers for the third example: $[1]$ $[2]$ $[3]$ $[4]$ \n\nAll valid answers for the fourth example: $[1, 2, 3, 7, 8, 9]$\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
},
{
"answer": "```python\nimport heapq\nn = int(input())\nd = list(map(int,input().split()))\npq = [-d[0]]\nheapq.heapify(pq)\nans = 0\nfor i in range(1,n):\n temp = i - d[i]\n heapq.heappush(pq,temp)\n if heapq.nsmallest(1,pq)[0] < temp:\n ans += temp - heapq.nsmallest(1,pq)[0]\n heapq.heappushpop(pq,temp)\nprint(ans)\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nSonya was unable to think of a story for this problem, so here comes the formal description.\n\nYou are given the array containing n positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0.\n\n\n-----Input-----\n\nThe first line of the input contains a single integer n (1 ≤ n ≤ 3000) — the length of the array.\n\nNext line contains n integer a_{i} (1 ≤ a_{i} ≤ 10^9).\n\n\n-----Output-----\n\nPrint the minimum number of operation required to make the array strictly increasing.\n\n\n-----Examples-----\nInput\n7\n2 1 5 11 5 9 11\n\nOutput\n9\n\nInput\n5\n5 4 3 2 1\n\nOutput\n12\n\n\n\n-----Note-----\n\nIn the first sample, the array is going to look as follows:\n\n2 3 5 6 7 9 11\n\n|2 - 2| + |1 - 3| + |5 - 5| + |11 - 6| + |5 - 7| + |9 - 9| + |11 - 11| = 9\n\nAnd for the second sample:\n\n1 2 3 4 5\n\n|5 - 1| + |4 - 2| + |3 - 3| + |2 - 4| + |1 - 5| = 12\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
}
] |
Solve the following coding problem using the programming language python:
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = s_{k} + 1s_{k} + 2... s_{n}s_1s_2... s_{k}. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
-----Input-----
The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.
-----Output-----
Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10^{ - 6}.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\frac{|a - b|}{\operatorname{max}(1,|b|)} \leq 10^{-6}$
-----Examples-----
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
-----Note-----
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
[
"```python\nstr = input()\nl = len(str)\na = [0] * (2 * l)\npos = [[] for i in range(26)]\nfor i, c in enumerate(str):\n t = ord(c) - ord('a')\n a[i] = t\n a[i + l] = t\n pos[t].append(i)\nans = 0\nfor c in range(26):\n cur = 0\n for k in range(1, l):\n cnt = [0] * 26\n for i in pos[c]:\n cnt[a[i + k]] += 1\n cur = max(cur, len(list([x for x in cnt if x == 1])))\n ans += cur\nprint(ans / l)\n\n```"
] |
[{"type": "stdin_stdout", "input": "technocup\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "tictictactac\n", "output": "0.333333333333333\n"}, {"type": "stdin_stdout", "input": "bbaabaabbb\n", "output": "0.100000000000000\n"}, {"type": "stdin_stdout", "input": "cbbbbcaaca\n", "output": "0.800000000000000\n"}, {"type": "stdin_stdout", "input": "cadbcdddda\n", "output": "0.800000000000000\n"}, {"type": "stdin_stdout", "input": "bababbdaee\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "fabbbhgedd\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "gaejllebhn\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaaaaabaaaabbb\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "eaaebccaeacdecaedcaabbbdeebccdcdaabeeaeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\n", "output": "0.080000000000000\n"}, {"type": "stdin_stdout", "input": "hcdhgcchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\n", "output": "0.450000000000000\n"}, {"type": "stdin_stdout", "input": "difhjdjbcdjedhiegagdejkbjfcdcdagdijdjajecbheiabfbjdgjdecfhdkgdbkcgcgakkiiggfkgcfadkjhiijkjacgejfhjge\n", "output": "0.840000000000000\n"}, {"type": "stdin_stdout", "input": "khjcoijiicdkdianmdolmadobdkcmgifdnffddnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\n", "output": "0.960000000000000\n"}, {"type": "stdin_stdout", "input": "kpsaloedscghjeaqadfhmlibjepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "jkeaagakbifeaechkifkdghcjcgighidcgdccfbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcegeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\n", "output": "0.438502673796791\n"}, {"type": "stdin_stdout", "input": "ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndciokabfaebjkndf\n", "output": "0.786096256684492\n"}, {"type": "stdin_stdout", "input": "aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbbbbaabbbbaaabbbbaaabbbb\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaab\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "abbacba\n", "output": "1.000000000000000\n"}]
| null |
null
|
You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests.
Solve the following coding problem using the programming language python:
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = s_{k} + 1s_{k} + 2... s_{n}s_1s_2... s_{k}. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
-----Input-----
The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.
-----Output-----
Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10^{ - 6}.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\frac{|a - b|}{\operatorname{max}(1,|b|)} \leq 10^{-6}$
-----Examples-----
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
-----Note-----
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT.
```python
# YOUR CODE HERE
```
### Answer: (use the provided format with backticks)
|
[{"type": "stdin_stdout", "input": "technocup\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "tictictactac\n", "output": "0.333333333333333\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bbaabaabbb\n", "output": "0.100000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "cbbbbcaaca\n", "output": "0.800000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "cadbcdddda\n", "output": "0.800000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bababbdaee\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "fabbbhgedd\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "gaejllebhn\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaaaaabaaaabbb\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "eaaebccaeacdecaedcaabbbdeebccdcdaabeeaeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\n", "output": "0.080000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "hcdhgcchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\n", "output": "0.450000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "difhjdjbcdjedhiegagdejkbjfcdcdagdijdjajecbheiabfbjdgjdecfhdkgdbkcgcgakkiiggfkgcfadkjhiijkjacgejfhjge\n", "output": "0.840000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "khjcoijiicdkdianmdolmadobdkcmgifdnffddnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\n", "output": "0.960000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "kpsaloedscghjeaqadfhmlibjepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "jkeaagakbifeaechkifkdghcjcgighidcgdccfbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcegeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\n", "output": "0.438502673796791\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndciokabfaebjkndf\n", "output": "0.786096256684492\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbbbbaabbbbaaabbbbaaabbbb\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaab\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "abbacba\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}]
|
livecodebench
|
deepcoder_6
| 6
|
[
{
"answer": "```python\ns = input()\nn = len(s)\nd = {}\nfor i in range(n):\n\tif s[i] not in d:\n\t\td[s[i]] = []\n\td[s[i]].append(s[i + 1:] + s[:i])\nres = 0\nfor (k, l) in d.items():\n\tans = 0\n\tfor j in range(n - 1):\n\t\t(seen, s1) = (set(), set())\n\t\tfor i in range(len(l)):\n\t\t\tif l[i][j] in s1:\n\t\t\t\ts1.remove(l[i][j])\n\t\t\telif l[i][j] not in seen:\n\t\t\t\ts1.add(l[i][j])\n\t\t\t\tseen.add(l[i][j])\n\t\tans = max(ans, len(s1))\n\tans /= n\n\tres += ans\nprint('{:.7f}'.format(res))\n\n```",
"question": "Solve the following coding problem using the programming language python:\n\nVasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.\n\nVasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. \n\nNote that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.\n\nInput\n\nThe only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.\n\nOutput\n\nPrint the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.\n\nFormally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>\n\nExamples\n\nInput\n\ntechnocup\n\n\nOutput\n\n1.000000000000000\n\n\nInput\n\ntictictactac\n\n\nOutput\n\n0.333333333333333\n\n\nInput\n\nbbaabaabbb\n\n\nOutput\n\n0.100000000000000\n\nNote\n\nIn the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.\n\nIn the second example if the first opened letter of t is \"t\" or \"c\", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is \"i\" or \"a\", then he can open the fourth letter and determine the shift uniquely.\n\nThe input will be stdin and you should print your solution to stdout\n\n\nNow solve the problem and return the code."
},
{
"answer": "```python\ns = input()\nn = len(s)\nd = {}\nfor i in range(n):\n if s[i] not in d: d[s[i]] = []\n d[s[i]].append(s[i + 1:] + s[:i])\nres = 0\nfor k, l in d.items():\n ans = 0\n for j in range(n - 1):\n seen, s1 = set(), set()\n for i in range(len(l)):\n if l[i][j] in s1: s1.remove(l[i][j])\n elif l[i][j] not in seen: \n s1.add(l[i][j])\n seen.add(l[i][j])\n ans = max(ans, len(s1))\n ans /= n\n res += ans\nprint('{:.7f}'.format(res))\n```",
"question": "Solve the following coding problem using the programming language python:\n\nVasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.\n\nVasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. \n\nNote that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.\n\nInput\n\nThe only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.\n\nOutput\n\nPrint the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.\n\nFormally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>\n\nExamples\n\nInput\n\ntechnocup\n\n\nOutput\n\n1.000000000000000\n\n\nInput\n\ntictictactac\n\n\nOutput\n\n0.333333333333333\n\n\nInput\n\nbbaabaabbb\n\n\nOutput\n\n0.100000000000000\n\nNote\n\nIn the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.\n\nIn the second example if the first opened letter of t is \"t\" or \"c\", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is \"i\" or \"a\", then he can open the fourth letter and determine the shift uniquely.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
},
{
"answer": "```python\ns=input()\n\nd=dict()\nmod=[]\nmx=[]\n\nfor k in s:\n\td[k]=[]\nfor i in range(len(s)):\n\td[s[i]].append(i)\nindex=0\nfor k in d.keys():\n\tmod.append(d[k])\n\nfor k in mod:\n\tmxct=0\n\tct=0\n\tx=[]\n\tfor i in range(len(s)):\n\t\tct=0\n\t\tdic=dict()\n\t\tfor j in k:\n\t\t\telt = s[(j+i)%(len(s))]\n\t\t\tif elt in dic.keys():\n\t\t\t\tdic[elt]+=1\n\t\t\telse:\n\t\t\t\tdic[elt]=1\n\t\tfor r in dic.keys():\n\t\t\tif dic[r]==1:\n\t\t\t\tct+=1\n\t\tmxct=max(ct,mxct)\n\tmx.append(mxct)\nsm=0\nfor k in mx:\n\tsm+=k\nprint(sm/len(s))\n```",
"question": "Solve the following coding problem using the programming language python:\n\nVasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.\n\nVasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. \n\nNote that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.\n\nInput\n\nThe only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.\n\nOutput\n\nPrint the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.\n\nFormally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>\n\nExamples\n\nInput\n\ntechnocup\n\n\nOutput\n\n1.000000000000000\n\n\nInput\n\ntictictactac\n\n\nOutput\n\n0.333333333333333\n\n\nInput\n\nbbaabaabbb\n\n\nOutput\n\n0.100000000000000\n\nNote\n\nIn the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.\n\nIn the second example if the first opened letter of t is \"t\" or \"c\", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is \"i\" or \"a\", then he can open the fourth letter and determine the shift uniquely.\n\nThe input will be given via stdin and the output should be printed to stdout by your code.\n\nNow solve the problem by providing the code."
}
] |
"Solve the following coding problem using the programming language python:\n\nIn the evenings Donkey(...TRUNCATED)
| ["```python\nfrom bisect import *\nfrom math import *\n\nn = int(input())\na, b, c, d = list(map(int(...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"15\\n1/3 2/1\\n3 1\\n6 2\\n4 2\\n2 5\\n4 5\\n6 6\\n3 4\\(...TRUNCATED)
| null |
null
| "You are an expert Python programmer. You will be given a question (problem specification) and will (...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"15\\n1/3 2/1\\n3 1\\n6 2\\n4 2\\n2 5\\n4 5\\n6 6\\n3 4\\(...TRUNCATED)
|
livecodebench
|
deepcoder_7
| 7
| [{"answer":"```python\nimport bisect\n\ndef INPUT():\n\tglobal n, a, b, c, d\n\tn = int(input())\n\t(...TRUNCATED)
|
"Solve the following coding problem using the programming language python:\n\nThe Little Elephant ha(...TRUNCATED)
| ["```python\nx = input ()\n\nflag = 0\ns = 0\n\nfor each_item in x:\n if each_item == '0':\n (...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"101\\n\", \"output\": \"11\\n\"}, {\"type\": \"stdin_std(...TRUNCATED)
| null |
null
| "You are an expert Python programmer. You will be given a question (problem specification) and will (...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"101\\n\", \"output\": \"11\\n\", \"metadata\": {\"func_n(...TRUNCATED)
|
livecodebench
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deepcoder_8
| 8
| [{"answer":"```python\ns = list(input())\nfor i in range(len(s)):\n\tif s[i] == '0':\n\t\tbreak\ndel(...TRUNCATED)
|
"Solve the following coding problem using the programming language python:\n\nIt is so boring in the(...TRUNCATED)
| ["```python\ndef gcd(a, b):\n while b > 0:\n a, b = b, a % b\n return a\n\nn = int(inpu(...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"2\\n2 3\\n\", \"output\": \"Alice\\n\"}, {\"type\": \"st(...TRUNCATED)
| null |
null
| "You are an expert Python programmer. You will be given a question (problem specification) and will (...TRUNCATED)
| "[{\"type\": \"stdin_stdout\", \"input\": \"2\\n2 3\\n\", \"output\": \"Alice\\n\", \"metadata\": {\(...TRUNCATED)
|
livecodebench
|
deepcoder_9
| 9
| [{"answer":"```python\nfrom sys import *\nfrom math import *\nfrom string import *\nfrom operator im(...TRUNCATED)
|
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