message stringlengths 2 57.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide. | instruction | 0 | 13,062 | 22 | 26,124 |
Tags: brute force, number theory
Correct Solution:
```
#! /usr/bin/env python3
import math
import sys
def lcm(u, v):
return u * v // math.gcd(u, v)
def main():
n, k = map(int, input().split())
m = 1
for i in range(1, k + 1):
m = lcm(m, i)
if m - 1 > n:
print('No')
sys.exit(0)
if (n + 1) % m == 0:
print('Yes')
else:
print('No')
if __name__ == '__main__':
main()
``` | output | 1 | 13,062 | 22 | 26,125 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide. | instruction | 0 | 13,063 | 22 | 26,126 |
Tags: brute force, number theory
Correct Solution:
```
import os, sys
from io import BytesIO, IOBase
from math import sqrt,ceil,gcd,log2
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
def dtb(n):
return bin(n).replace("0b", "")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def lcm(a,b):
return a*b//gcd(a,b)
n,k=map(int,input().split())
s=set()
for i in range(1,min(50,k)+1):
s.add(n%i)
if len(s)==min(50,k):
print('YES')
else:
print('NO')
``` | output | 1 | 13,063 | 22 | 26,127 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide. | instruction | 0 | 13,064 | 22 | 26,128 |
Tags: brute force, number theory
Correct Solution:
```
import bisect
from itertools import accumulate, count
import os
import sys
import math
from decimal import *
from io import BytesIO, IOBase
from sys import maxsize
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input():
return sys.stdin.readline().rstrip("\r\n")
def isPrime(n):
if n <= 1:
return False
if n <= 3:
return True
if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
if n % i == 0 or n % (i + 2) == 0:
return False
i = i + 6
return True
def SieveOfEratosthenes(n):
prime = []
primes = [True for i in range(n + 1)]
p = 2
while p * p <= n:
if primes[p] == True:
prime.append(p)
for i in range(p * p, n + 1, p):
primes[i] = False
p += 1
return prime
def primefactors(n):
fac = []
while n % 2 == 0:
fac.append(2)
n = n // 2
for i in range(3, int(math.sqrt(n)) + 2):
while n % i == 0:
fac.append(i)
n = n // i
if n > 1:
fac.append(n)
return sorted(fac)
def factors(n):
fac = set()
fac.add(1)
fac.add(n)
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
fac.add(i)
fac.add(n // i)
return list(fac)
def modInverse(a, m):
m0 = m
y = 0
x = 1
if m == 1:
return 0
while a > 1:
q = a // m
t = m
m = a % m
a = t
t = y
y = x - q * y
x = t
if x < 0:
x = x + m0
return x
# -----------------------------------------------------code
n,k=map(int,input().split())
if k>70:
print("No")
else:
s=set()
for i in range(1,k+1):
s.add(n%i)
if len(s)==k:
print("Yes")
else:
print("No")
``` | output | 1 | 13,064 | 22 | 26,129 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide. | instruction | 0 | 13,065 | 22 | 26,130 |
Tags: brute force, number theory
Correct Solution:
```
n,k = map(int,input().split())
if k==1:
print("Yes")
elif n==1:
if k<=2:
print("Yes")
else:
print("No")
elif k>=n:
print("No")
else:
if n%2==0:
print("No")
else:
ans=0
rem=[0]*(100010)
for i in range(1,100002):
if rem[n%i]==0:
ans+=1
rem[n%i]=1
# print(n%i,i)
else:
break
if ans>=k:
print("Yes")
else:
print("No")
``` | output | 1 | 13,065 | 22 | 26,131 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide. | instruction | 0 | 13,066 | 22 | 26,132 |
Tags: brute force, number theory
Correct Solution:
```
n, k = map(int, input().strip().split())
if k == 1:
print('Yes')
else:
# k! - 1 must divide into n
'''
prod = 1
count = 2
while prod < n:
prod *= count
if n % (prod - 1) == 0 and count >= k:
#res = n // (prod - 1)
# note: existance means k must be really small
rems = [n % i for i in range(1, k + 1)]
#print(rems)
if len(set(rems)) == len(rems):
print('Yes')
break
count += 1
else:
print('No')
'''
if k > 50000:
print('No')
else:
rems = [n % i for i in range(1, k + 1)]
#print(rems)
print('Yes' if len(set(rems)) == len(rems) else 'No')
``` | output | 1 | 13,066 | 22 | 26,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
def gcd(x,y):
if y==0:
return x
return gcd(y,x%y)
def lcm(x,y):
return x//gcd(x,y)*y
a=input().split()
n,k=int(a[0]),int(a[1])
ans=1
for x in range(1,k+1):
ans=lcm(ans,x)
if ans>n+1:
print("No")
exit(0)
if (n+1)%ans==0:
print("Yes")
else:
print("No")
``` | instruction | 0 | 13,067 | 22 | 26,134 |
Yes | output | 1 | 13,067 | 22 | 26,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
def first_fail(n):
assert n >= 2
was = set()
for k in range(1, n + 1):
mod = n % k
if mod in was:
return k
was.add(mod)
assert False, n
def solve(n, k):
if n == 1:
return k <= 2
return k < first_fail(n)
n, k = [int(v) for v in input().split()]
print(["No", "Yes"][solve(n, k)])
``` | instruction | 0 | 13,068 | 22 | 26,136 |
Yes | output | 1 | 13,068 | 22 | 26,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
n, k = map(int, input().split())
for i in range(1, k + 1):
if n % i != i - 1:
print("NO")
exit()
print("YES")
``` | instruction | 0 | 13,069 | 22 | 26,138 |
Yes | output | 1 | 13,069 | 22 | 26,139 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
import getpass
import sys
import math
def ria():
return [int(i) for i in input().split()]
files = True
if getpass.getuser() == 'frohenk' and files:
sys.stdin = open("test.in")
# sys.stdout = open('test.out', 'w')
n, k = ria()
if k > 100:
print('No')
exit(0)
mp = {}
for i in range(1, k + 1):
mp[n % i] = 1
if len(mp) == k:
print('Yes')
else:
print('No')
sys.stdout.close()
``` | instruction | 0 | 13,070 | 22 | 26,140 |
Yes | output | 1 | 13,070 | 22 | 26,141 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
n = input().split()
n, k = int(n[0]), int(n[1])
s = "Yes"
if k >= n:
s = "No"
else:
for i in range(1, k+1):
if (n%i != i-1):
s = "No"
break
print(s)
``` | instruction | 0 | 13,071 | 22 | 26,142 |
No | output | 1 | 13,071 | 22 | 26,143 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
values = input()
n, k = values.split()
n = int(n)
k = int(k)
old = -1
if(k >= n):
print("No")
else:
distinct = True
for i in range(1, k + 1):
res = n%i
if(old == -1):
old = res
elif(res == old):
print("No")
distinct = False
old = res
break
if(distinct):
print("Yes")
``` | instruction | 0 | 13,072 | 22 | 26,144 |
No | output | 1 | 13,072 | 22 | 26,145 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
n,k=map(int,input().split())
if n==1 or k==1:
if n==1 and k==1:
print("Yes")
elif n==1:
print("No")
else:
print("Yes")
elif k>=n:
print("No")
else:
i=1
while i<=k and n%i==i-1:
i+=1
if i==k+1:
print("Yes")
else:
print("No")
``` | instruction | 0 | 13,073 | 22 | 26,146 |
No | output | 1 | 13,073 | 22 | 26,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Imp is watching a documentary about cave painting.
<image>
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all <image>, 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:
* 1 ≤ i < j ≤ k,
* <image>, where <image> is the remainder of division x by y.
Input
The only line contains two integers n, k (1 ≤ n, k ≤ 1018).
Output
Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper).
Examples
Input
4 4
Output
No
Input
5 3
Output
Yes
Note
In the first sample remainders modulo 1 and 4 coincide.
Submitted Solution:
```
a,b = map(int,input().split())
if(a%b==b%a):
print("No")
else:
print("Yes")
``` | instruction | 0 | 13,074 | 22 | 26,148 |
No | output | 1 | 13,074 | 22 | 26,149 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,343 | 22 | 26,686 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Tue Nov 13 20:48:59 2018
@author:
"""
n=int(input())
l=list(map(int,input().split()))
l.sort()
s=0
for i in range(n//2):
s+=(l[i]+l[n-i-1])**2
print(s)
``` | output | 1 | 13,343 | 22 | 26,687 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,344 | 22 | 26,688 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n=int(input())
s=list(map(int,input().split()))
s.sort()
m=list(reversed(s))
sum=0
for i in range(n//2):
sum+=(s[i]+m[i])**2
print(sum)
``` | output | 1 | 13,344 | 22 | 26,689 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,345 | 22 | 26,690 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n=int(input())
a=[int(s) for s in input().split(' ')]
a.sort()
min_sum=0
for i in range(len(a)):
min_sum+=(a[i]+a[n-1-i])**2
print(int(min_sum/2))
``` | output | 1 | 13,345 | 22 | 26,691 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,346 | 22 | 26,692 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n = int(input())
l = list(map(int, input().split()))
l.sort()
o = 0
a = 0
for i in range(n // 2):
a = l[i] + l[- (i + 1)]
o += a * a
print(o)
``` | output | 1 | 13,346 | 22 | 26,693 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,347 | 22 | 26,694 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n = int(input())
#n, m = map(int, input().split())
arr = sorted(map(int, input().split()))
s = 0
for i in range(len(arr)//2):
s += (arr[i]+arr[(-i-1)]) ** 2
print(s)
``` | output | 1 | 13,347 | 22 | 26,695 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,348 | 22 | 26,696 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n=int(input())
s=input()
a=s.split(" ")
a=list(map(int,a))
a.sort()
out=list()
for i in range(int(n/2)):
s=int(a[i]+a[n-i-1])
out.append(s)
if n%2!=0:
out[int(len(out)-1)]=out[int(len(out)-1)]+a[int(n/2)]
output=0
for i in range(len(out)):
output=output+out[i]*out[i]
print(output)
``` | output | 1 | 13,348 | 22 | 26,697 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,349 | 22 | 26,698 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
n = int(input())
seq = sorted(list(map(int, input().split())))
ans = 0
for i in range(n // 2):
ans += (seq[i] + seq[-(i + 1)])**2
print(ans)
``` | output | 1 | 13,349 | 22 | 26,699 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27. | instruction | 0 | 13,350 | 22 | 26,700 |
Tags: greedy, implementation, math, sortings
Correct Solution:
```
# list(map(int, input().split()))
n = int(input())
numbers = list(map(int, input().split()))
numbers = sorted(numbers)
ans = 0
for i in range(n // 2):
ans += (numbers[i] + numbers[n - i - 1]) ** 2
print(ans)
``` | output | 1 | 13,350 | 22 | 26,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
def inpl(): return list(map(int, input().split()))
N = int(input())
A = inpl()
A.sort()
print(sum([(i+j)**2 for i, j in zip(A[:N//2], A[::-1][:N//2])]))
``` | instruction | 0 | 13,351 | 22 | 26,702 |
Yes | output | 1 | 13,351 | 22 | 26,703 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
n = int(input())
l = [*map(int, input().split())]
l.sort()
i, j = 0, n - 1
res = 0
while i <= j:
res += (l[i] + l[j]) ** 2
i += 1
j -= 1
print(res)
``` | instruction | 0 | 13,352 | 22 | 26,704 |
Yes | output | 1 | 13,352 | 22 | 26,705 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
# import sys
# sys.stdin = open("test.in","r")
# sys.stdout = open("test.out","w")
n=int(input())
a=sorted(map(int,input().split()))
c=0
for i in range(n//2):
c+=(a[i]+a[n-1-i])**2
print(c)
``` | instruction | 0 | 13,353 | 22 | 26,706 |
Yes | output | 1 | 13,353 | 22 | 26,707 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
n=int(input())
a=[*map(int,input().split())]
a.sort()
i=0
ans=0
while i<n:
ans+=(a[i]+a[n-i-1])*(a[i]+a[n-i-1])
i+=1
ans=int(ans/2)
print(ans)
``` | instruction | 0 | 13,354 | 22 | 26,708 |
Yes | output | 1 | 13,354 | 22 | 26,709 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
# Collaborated with Rudransh
inp = input()
n = int(inp)
inp = input().split(" ")
a = []
sum = 0
for i in inp:
a.append(int(i))
a.sort()
for i in range(n):
sum += pow(a[i] + a[n - i - 1], 2)
print(sum/2)
``` | instruction | 0 | 13,355 | 22 | 26,710 |
No | output | 1 | 13,355 | 22 | 26,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
n=int(input())
s=input().split()
s.sort()
summ=0
for i in range(n//2):
summ=summ+(int(s[i])+int(s[n-1-i]))**2
print(summ)
``` | instruction | 0 | 13,356 | 22 | 26,712 |
No | output | 1 | 13,356 | 22 | 26,713 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
import heapq
n = int(input())
g = n//2
nums = list(map(int,input().split()))
nums = sorted(nums,reverse = True)
groups = [float("inf")]+[0 for _ in range(g)]+[float("inf")]
i = 1
h = [(0,_+1) for _ in range(g)]
heapq.heapify(h)
for num in nums:
total,i = heapq.heappop(h)
groups[i] += num
heapq.heappush(h,(groups[i],i))
print (sum(x**2 for x in groups[1:-1]))
``` | instruction | 0 | 13,357 | 22 | 26,714 |
No | output | 1 | 13,357 | 22 | 26,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
Submitted Solution:
```
n=int(input())
s=input().split()
s=list(s)
for i in range(n):
s[i]=int(s[i])
s.sort()
sum=0
print(*s)
for i in range(n//2):
sum+=((s[i]) + s[n-1-i])**2
print(sum)
``` | instruction | 0 | 13,358 | 22 | 26,716 |
No | output | 1 | 13,358 | 22 | 26,717 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,500 | 22 | 27,000 |
Tags: brute force, math, number theory
Correct Solution:
```
import math
def pf(n):
fac = {}
while n % 2 == 0:
fac[2] = fac.get(2, 0)+1
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
fac[i] = fac.get(i, 0)+1
n = n // i
if n > 2:
fac[n] = fac.get(n, 0)+1
return fac
def gp(f, p):
s = 1
e = int(math.ceil(math.log(p,f)))
val = 1
while(s<=e):
mid = (s+e)//2
if p%(f**mid)!=0:
e = mid - 1
else:
s = mid+1
val = mid
return val
test = int(input())
for _ in range(test):
p, q = map(int, input().split())
if p%q:
print(p)
else:
pfac = pf(q)
val = float("inf")
for k in pfac:
u = gp(k, p)
val = min(val, (k**(u-pfac[k]+1)))
ans = p//val
print(ans)
``` | output | 1 | 13,500 | 22 | 27,001 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,501 | 22 | 27,002 |
Tags: brute force, math, number theory
Correct Solution:
```
from sys import stdin, stdout
from math import sqrt
#stdin = open('Q3.txt', 'r')
def II(): return int(stdin.readline())
def MI(): return map(int, stdin.readline().split())
bigp=10**18+7
primes=[]
def SieveOfEratosthenes(n,primes):
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
for p in range(2, n):
if prime[p]:
primes.append(p)
def solve():
p,q=MI()
if p%q != 0:
ans=p
else:
x,y=q,p
mind=bigp
sqrtq=int(sqrt(q))
sp=[i for i in primes if i<=sqrtq]+[bigp]
for i in sp:
j=i
if x==1:
break
qe=0
while x%j==0:
qe+=1
x=x//j
if i==bigp:
qe,j=1,x
if qe>0:
pe=qe
y=y//pow(j,qe)
while y%j==0:
pe+=1
y=y//j
mind=min(mind,pow(j,pe-qe+1))
ans=p//mind
stdout.write(str(ans)+"\n")
SieveOfEratosthenes(32000,primes)
t=II()
for _ in range(t):
solve()
``` | output | 1 | 13,501 | 22 | 27,003 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,502 | 22 | 27,004 |
Tags: brute force, math, number theory
Correct Solution:
```
import sys
#from collections import deque
#from functools import *
#from fractions import Fraction as f
from copy import *
from bisect import *
#from heapq import *
from math import gcd,ceil,sqrt
from itertools import permutations as prm,product
def eprint(*args):
print(*args, file=sys.stderr)
zz=1
#sys.setrecursionlimit(10**6)
if zz:
input=sys.stdin.readline
else:
sys.stdin=open('input.txt', 'r')
sys.stdout=open('all.txt','w')
di=[[-1,0],[1,0],[0,1],[0,-1]]
def string(s):
return "".join(s)
def fori(n):
return [fi() for i in range(n)]
def inc(d,c,x=1):
d[c]=d[c]+x if c in d else x
def bo(i):
return ord(i)-ord('A')
def li():
return [int(xx) for xx in input().split()]
def fli():
return [float(x) for x in input().split()]
def comp(a,b):
if(a>b):
return 2
return 2 if a==b else 0
def gi():
return [xx for xx in input().split()]
def cil(n,m):
return n//m+int(n%m>0)
def fi():
return int(input())
def pro(a):
return reduce(lambda a,b:a*b,a)
def swap(a,i,j):
a[i],a[j]=a[j],a[i]
def si():
return list(input().rstrip())
def mi():
return map(int,input().split())
def gh():
sys.stdout.flush()
def isvalid(i,j,n,m):
return 0<=i<n and 0<=j<m
def bo(i):
return ord(i)-ord('a')
def graph(n,m):
for i in range(m):
x,y=mi()
a[x].append(y)
a[y].append(x)
t=fi()
while t>0:
t-=1
p,q=mi()
d={}
if p%q:
print(p)
else:
for j in range(2,ceil(sqrt(q))+3):
if q%j==0:
d[j]=0
while q%j==0:
q//=j
d[j]+=1
if q>=2:
d[q]=1
mini=10**18
n=p
for i in d:
c=0
if p%i==0:
while p%i==0:
p//=i
c+=1
mini=min(mini,i**(c-d[i]+1))
print(n//mini)
``` | output | 1 | 13,502 | 22 | 27,005 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,503 | 22 | 27,006 |
Tags: brute force, math, number theory
Correct Solution:
```
from sys import stdin,stdout
from collections import *
from math import gcd,floor,ceil
st=lambda:list(stdin.readline().strip())
li=lambda:list(map(int,stdin.readline().split()))
mp=lambda:map(int,stdin.readline().split())
inp=lambda:int(stdin.readline())
pr=lambda n: stdout.write(str(n)+"\n")
INF=float('inf')
def factors(n):
l=[]
i=2
while i*i<=n:
if n%i==0:
x=[i,0]
while n%i==0:
n//=i
x[1]+=1
l.append(x)
i+=1
if n>1:
l.append([n,1])
return l
def solve():
a,b=mp()
if a%b:
pr(a)
return
fact=factors(b)
mi=a
for i in fact:
p=a
count=0
while p%i[0]==0:
count+=1
p//=i[0]
cur=1
while count >= i[1]:
cur*=i[0]
count-=1
mi=min(mi,cur)
pr(a//mi)
for _ in range(inp()):
solve()
``` | output | 1 | 13,503 | 22 | 27,007 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,504 | 22 | 27,008 |
Tags: brute force, math, number theory
Correct Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key,lru_cache
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# import sys
# input = sys.stdin.readline
M = mod = 10**9 + 7
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().rstrip().split()]
def st():return str(input().rstrip())[2:-1]
def val():return int(input().rstrip())
def li2():return [str(i)[2:-1] for i in input().rstrip().split()]
def li3():return [int(i) for i in st()]
def factorize(n):
d = defaultdict(int)
for i in range(2, int(n ** 0.5) + 1):
while n % i == 0:
d[i] += 1
n = n // i
if n - 1:d[n] = 1
return d
for i in range(val()):
a, b = li()
if a % b:
print(a)
continue
mydict = factorize(b)
l = list(mydict)
ans = a
finans = 1
for i in l:
temp = ans
while temp % i == 0:temp = temp // i
temp *= i ** (mydict[i] - 1)
finans = max(finans, temp)
print(finans)
``` | output | 1 | 13,504 | 22 | 27,009 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,505 | 22 | 27,010 |
Tags: brute force, math, number theory
Correct Solution:
```
for _ in range(int(input())):
p, q = map(int,input().split())
c = q
d = p
i = 1
factor = []
while i*i <= q:
if q % i == 0:
factor.append(i)
if q//i != i:
factor.append(q//i)
i += 1
factor.sort(reverse=True)
factor.pop()
m = 1
for i in factor:
d = p
while d % c == 0:
d //= i
m = max(m, d)
print(m)
``` | output | 1 | 13,505 | 22 | 27,011 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,506 | 22 | 27,012 |
Tags: brute force, math, number theory
Correct Solution:
```
T=int(input())
for _ in range(T):
p,q=map(int,input().split())
if p<q:
print(p)
elif p%q!=0:
print(p)
else:
s=set()
i=2
while i*i<=q:
if q%i==0:
s.add(i)
s.add(q//i)
i+=1
s.add(q)
l=list(s)
#print(l)
lis=[1]
for i in l:
ch=p
while ch%i==0:
ch//=i
if ch%q:
lis.append(ch)
break
print(max(lis))
``` | output | 1 | 13,506 | 22 | 27,013 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6. | instruction | 0 | 13,507 | 22 | 27,014 |
Tags: brute force, math, number theory
Correct Solution:
```
"""T=int(input())
for _ in range(0,T):
n=int(input())
a,b=map(int,input().split())
s=input()
s=[int(x) for x in input().split()]
for i in range(0,len(s)):
a,b=map(int,input().split())"""
import math
T=int(input())
for _ in range(0,T):
p,q=map(int,input().split())
if(p%q!=0):
print(p)
else:
n = q
L=[]
if(n%2==0):
L.append(2)
while(n%2==0):
n=n//2
for i in range(3,int(math.sqrt(n))+1,2):
if(n%i==0):
L.append(i)
while(n%i==0):
n=n//i
if(n>2):
L.append(n)
ans=1
for i in range(0,len(L)):
num=p
ele=L[i]
while(num%q==0 and num%ele==0):
num=num//ele
ans=max(ans, num)
print(ans)
``` | output | 1 | 13,507 | 22 | 27,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""
import os
import sys
from io import BytesIO, IOBase
import heapq as h
from bisect import bisect_left, bisect_right
from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
self.os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
from collections import defaultdict as dd, deque as dq
import math, string
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input()
def listStr():
return list(input())
MOD = 10**9+7
"""
Start with P
P has factors pi**qi
X = P, is X % Q == 0, doesn't work
Need the largest factor of P s.t. factor % Q = 0
30
10
1 2 3 5 6 10 15 30 so 15 is the answer
If P//Q is the smallest factor of P, the answer is the next smallest factor
Otherwise, the answer is either the next factor, or a smaller factor which doesn't divide P//Q
We need to remove a combination of factors from P until it doesn't divide Q any more
50 = 2*2*5
100 = 2*2*5*5
10 = 2*5
30 = 2*3*5
Answer = 5*5
"""
from functools import reduce
def factors(n):
return set(reduce(list.__add__,
([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def solve():
P, Q = getInts()
if P < Q:
return P
if P % Q > 0:
return P
facs = sorted(list(factors(Q)))
best = 0
for fac in facs:
if fac == 1:
continue
power = 1
while P % fac**power == 0:
#print(P,fac,power,flush=True)
tmp = P//(fac**power)
if tmp % Q > 0:
best = max(best,tmp)
power += 1
return best
for _ in range(getInt()):
print(solve())
``` | instruction | 0 | 13,508 | 22 | 27,016 |
Yes | output | 1 | 13,508 | 22 | 27,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**5)
int1 = lambda x: int(x)-1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.buffer.readline())
def MI(): return map(int, sys.stdin.buffer.readline().split())
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def BI(): return sys.stdin.buffer.readline().rstrip()
def SI(): return sys.stdin.buffer.readline().rstrip().decode()
def PrimeFactorization(x):
def plist(x):
if x < 2: return []
if x & 1 == 0: return [2] + plist(x >> 1)
for p in range(3, x + 1, 2):
if x % p == 0: return [p] + plist(x // p)
if p ** 2 > x: return [x]
pl = plist(x)
pp, ee = [], []
for p in pl:
if not pp or p != pp[-1]:
pp += [p]
ee += [0]
ee[-1] += 1
return [(p, e) for p, e in zip(pp, ee)]
def solve():
if p%q:return p
be=PrimeFactorization(q)
mn=p
for b,e in be:
c=p
c//=b**e
cur=b
while c%b==0:
cur*=b
c//=b
mn=min(mn,cur)
return p//mn
for _ in range(II()):
p,q=MI()
print(solve())
``` | instruction | 0 | 13,509 | 22 | 27,018 |
Yes | output | 1 | 13,509 | 22 | 27,019 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
## necessary imports
import sys
input = sys.stdin.readline
# biesect_left is essentially an equivalent of lower_bound function in
# cpp and returns the first index not smaller than x.
from bisect import bisect_left;
from bisect import bisect_right;
from math import ceil, factorial;
def ceil(x):
if x != int(x):
x = int(x) + 1;
return x;
# swap_array function
def swaparr(arr, a,b):
temp = arr[a];
arr[a] = arr[b];
arr[b] = temp;
## gcd function
def gcd(a,b):
if b == 0:
return a;
return gcd(b, a % b);
## nCr function efficient using Binomial Cofficient
def nCr(n, k, modulus = 1):
if(k > n - k):
k = n - k;
res = 1;
for i in range(k):
res = res * (n - i);
res = res / (i + 1);
res %= modulus;
return int(res);
## prime factorization
def primefs(n):
## if n == 1 ## calculating primes
primes = {}
while(n%2 == 0 and n > 0):
primes[2] = primes.get(2, 0) + 1
n = n//2
for i in range(3, int(n**0.5)+2, 2):
while(n%i == 0 and n > 0):
primes[i] = primes.get(i, 0) + 1
n = n//i
if n > 2:
primes[n] = primes.get(n, 0) + 1
## prime factoriazation of n is stored in dictionary
## primes and can be accesed. O(sqrt n)
return primes
## MODULAR EXPONENTIATION FUNCTION
def power(x, y, p):
res = 1
x = x % p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) :
res = (res * x) % p
y = y >> 1
x = (x * x) % p
return res
## DISJOINT SET UNINON FUNCTIONS
def swap(a,b):
temp = a
a = b
b = temp
return a,b;
# find function with path compression included (recursive)
# def find(x, link):
# if link[x] == x:
# return x
# link[x] = find(link[x], link);
# return link[x];
# find function with path compression (ITERATIVE)
def find(x, link):
p = x;
while( p != link[p]):
p = link[p];
while( x != p):
nex = link[x];
link[x] = p;
x = nex;
return p;
# the union function which makes union(x,y)
# of two nodes x and y
def union(x, y, link, size):
x = find(x, link)
y = find(y, link)
if size[x] < size[y]:
x,y = swap(x,y)
if x != y:
size[x] += size[y]
link[y] = x
## returns an array of boolean if primes or not USING SIEVE OF ERATOSTHANES
def sieve(n):
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
return prime
#### PRIME FACTORIZATION IN O(log n) using Sieve ####
MAXN = int(1e6 + 5)
def spf_sieve():
spf[1] = 1;
for i in range(2, MAXN):
spf[i] = i;
for i in range(4, MAXN, 2):
spf[i] = 2;
for i in range(3, ceil(MAXN ** 0.5), 2):
if spf[i] == i:
for j in range(i*i, MAXN, i):
if spf[j] == j:
spf[j] = i;
## function for storing smallest prime factors (spf) in the array
################## un-comment below 2 lines when using factorization #################
# spf = [0 for i in range(MAXN)]
# spf_sieve();
def factoriazation(x):
ret = {};
while x != 1:
ret[spf[x]] = ret.get(spf[x], 0) + 1;
x = x//spf[x]
return ret;
## this function is useful for multiple queries only, o/w use
## primefs function above. complexity O(log n)
## taking integer array input
def int_array():
return list(map(int, input().strip().split()));
def float_array():
return list(map(float, input().strip().split()));
## taking string array input
def str_array():
return input().strip().split();
#defining a couple constants
MOD = int(1e9)+7;
CMOD = 998244353;
INF = float('inf'); NINF = -float('inf');
################### ---------------- TEMPLATE ENDS HERE ---------------- ###################
for _ in range(int(input())):
p, q = int_array();
if q > p or p % q != 0:
print(p);
continue;
fact = primefs(q);
ans = NINF;
for i in fact:
x = p;
while x % q == 0:
x //= i;
ans = max(ans, x);
print(ans);
``` | instruction | 0 | 13,510 | 22 | 27,020 |
Yes | output | 1 | 13,510 | 22 | 27,021 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
import math
for i in range(int(input())):
p,q=map(int,input().split())
l=p
if p%q!=0:
print(p)
else:
g=[]
c=1
if q%2==0:
while q%2==0:
q=q//2
p=p//2
while p%2==0:
c=c*2
p=p//2
g.append(c*2)
for j in range(3,int(math.sqrt(q))+2,2):
if q%j==0:
c=1
while q%j==0:
q=q//j
p=p//j
while p%j==0:
c=c*j
p=p//j
g.append(c*j)
if q>2:
c=1
while p%q==0:
c=c*q
p=p//q
g.append(c)
print(l//(min(g)))
``` | instruction | 0 | 13,511 | 22 | 27,022 |
Yes | output | 1 | 13,511 | 22 | 27,023 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
import math
def smallestDivisor(n):
if (n % 2 == 0):
return 2;
i = 3;
while(i * i <= n):
if (n % i == 0):
return i;
i += 2;
return n;
def prevPowerofK(n, k):
p = int(math.log(n) / math.log(k))
return int(math.pow(k, p))
def primeFactors(n):
l = []
while n % 2 == 0:
l.append(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
l.append(i)
n = n // i
if n > 2:
l.append(n)
return l
t = int(input())
while t:
n,x= map(int,input().split())
if n>x:
if n%x!=0:
print(n)
else:
l2 = primeFactors(x)
d2 = {}
for j in l2:
if j in d2:
d2[j]+=1
else:
d2[j]=1
ans = 0
for i in d2:
if n%i==0:
power = 1
number = i
while n%number==0:
power+=1
number *=i
xxx = n// i**(power-1)
xxx *= i**(d2[i]-1)
ans = max(ans,xxx)
print(ans)
else:
print(n)
t-=1
``` | instruction | 0 | 13,512 | 22 | 27,024 |
No | output | 1 | 13,512 | 22 | 27,025 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
import math
''' Get all the prime factors '''
def prime_factorization(x):
result = []
for i in range(2, int(math.sqrt(x)) + 1):
# If 'i' is a divisor of 'x',
if x % i == 0:
# Count how many times 'i' can divide 'x' consecutively.
count = 0
while x % i == 0:
count += 1
x //= i
result.append((i, count))
if x > 1:
result.append((x, 1))
return result
''' Find all divisors of a number '''
def find_all_divisors_of_a_number(x):
result = []
for i in range(1, int(math.sqrt(x)) + 1):
if x % i == 0:
result.append(i)
if i * i != x:
result.append(x // i)
return result
for _ in range(int(input())):
p, q = map(int, input().split())
if p < q:
print(p)
else:
if p % q != 0:
print(p)
else:
now = prime_factorization(q)
max_value = 0
for i in now:
cur = p
prime = i[0]
cnt = i[1]
while cur % (prime ** cnt) == 0:
cur /= prime
max_value = max(max_value, int(cur))
print(max_value)
``` | instruction | 0 | 13,513 | 22 | 27,026 |
No | output | 1 | 13,513 | 22 | 27,027 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
import sys
import math
def II():
return int(sys.stdin.readline())
def LI():
return list(map(int, sys.stdin.readline().split()))
def MI():
return map(int, sys.stdin.readline().split())
def SI():
return sys.stdin.readline().strip()
t = II()
for q in range(t):
p,q = MI()
q2 = q
a = []
while True:
count = 0
for i in range(2,int(q**0.5)+1):
if q%i == 0:
count+=1
a.append(i)
q//=i
break
if count == 0:
a.append(q)
break
ans = []
while p%q2 == 0:
p//=q2
ans+=a
if ans:
ans.sort(reverse=True)
while True:
count = 0
for i in range(len(ans)):
if p*ans[i]%q2!=0:
p*=ans[i]
count = 1
ans.pop(i)
break
if count == 0:
break
print(p)
``` | instruction | 0 | 13,514 | 22 | 27,028 |
No | output | 1 | 13,514 | 22 | 27,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
Submitted Solution:
```
from sys import stdin, gettrace
if gettrace():
inputi = input
else:
def input():
return next(stdin)[:-1]
def inputi():
return stdin.buffer.readline()
def solve():
p, q = map(int, inputi().split())
if p%q != 0:
print(p)
return
qf = {}
qr = q
i = 2
while i*i < qr:
while qr%i == 0:
qf[i] = qf.get(i, 0) + 1
qr //= i
i+=1
if qr != 1:
qf[qr] = 1
pf = {}
pr = p
for f in qf.keys():
pf[f] = 0
while pr%f == 0:
pf[f] += 1
pr //= f
best = 0
for f in qf.keys():
best = max(p//(f**(pf[f] -qf[f]+1)), best)
print(best)
def main():
t = int(inputi())
for _ in range(t):
solve()
if __name__ == "__main__":
main()
``` | instruction | 0 | 13,515 | 22 | 27,030 |
No | output | 1 | 13,515 | 22 | 27,031 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
inp = input().split(' ')
def result(sets,maximum_divisor):
output = list()
output.append(str(int(maximum_divisor) * (6 * int(sets) - 1)))
for i in range(int(sets)):
output.append(str(int(maximum_divisor)* (6 * int(i) + 1)) + ' ' + str(int(maximum_divisor) * (6 * int(i) + 3)) + ' ' + str(int(maximum_divisor) * (6 * int(i) + 4)) + ' ' + str(int(maximum_divisor) * (6 * int(i) + 5)))
return output
for i in result(inp[0],inp[1]):
print(i)
``` | instruction | 0 | 13,682 | 22 | 27,364 |
Yes | output | 1 | 13,682 | 22 | 27,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
inp = input().split(' ')
def result(sets, maximum_divisor):
maximum_divisor = 7
sets = 9
output = list()
output.append(str(int(maximum_divisor) * (6 * int(sets) - 1)))
for i in range(int(sets)):
output.append(str(int(maximum_divisor) * (6 * int(i) + 1)) + ' ' + str(int(maximum_divisor) * (6 * int(i) + 3)) +
' ' + str(int(maximum_divisor) * (6 * int(i) + 4)) + ' ' + str(int(maximum_divisor) * (6 * int(i) + 5)))
return output
for i in result(inp[0], inp[1]):
print(i)
``` | instruction | 0 | 13,684 | 22 | 27,368 |
No | output | 1 | 13,684 | 22 | 27,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
__author__ = 'neki'
import sys
import math
#sys.stdin = open("sets.in", "r")
global primes, primeDiv
def primality(limit):
global primes, primeDiv
primes = [2, 3]
primeDiv = [[], [], [], []] #according to an abstraction made: 0, 1, 2, 3 have no prime divisors
i = 4
k = 3 #we can use 1, 2 and 3, we need limit prime numbers to be absolutely sure we cannot fail
while k < limit:
primeDiv.append([])
for j in primes:
if 2*j > i:
break
if i % j == 0:
primeDiv[i].append(j)
if not primeDiv[i]:
primes.append(i)
k += 1
i += 1
def gcdPrime(a, b):
if b==0 or a==0:
return 0 #not prime
if b==1 or a==1:
return 1 #prime
if b>a:
return gcdPrime(a, b%a)
return gcdPrime(b, a%b)
def gcdPrimeSet(set, a):
result = []
if len(set) >= 4: #full set
return [x for x in set]
for i in set:
if gcdPrime(i, a) == 0:
result.append(i)
return result
words = str(input()).split()
n = int(words[0])
k = int(words[1])
primality(4*n)
#print(primes)
#print(primeDiv)
#print(gcdPrime(8, 12))
sets = []
for i in range(n):
sets.append(set())
m = 0
nEl = 0
iniSet = 0
stack = [2]
last = 2
stPointer = 0
while nEl < 4*n-1:
m = stack[stPointer]
#print(m, sets)
sw = 0
setProblems = [[] for x in sets]
for j in range(iniSet, iniSet + len(sets)):
i = j % len(sets)
setProblems[i] = gcdPrimeSet(sets[i], m)
if len(setProblems[i]) == 0:
sets[i].add(m)
last += 1
stack.append(last)
iniSet += 1
nEl += 1
sw = 1
break
if sw == 0:
for i in range(len(setProblems)):
if len(setProblems[i]) == 1 and len(primeDiv[m]) < len(primeDiv[setProblems[i][0]]):
sets[i].remove(setProblems[i][0])
sets[i].add(m)
stack.append(setProblems[i][0])
break
else:
last += 1
stack.append(last)
stPointer += 1
print(k*m)
for s in sets:
if len(s) < 4:
s.add(1)
for s in sets:
for i in range(4):
print(k*s.pop(), end=" ")
print()
``` | instruction | 0 | 13,685 | 22 | 27,370 |
No | output | 1 | 13,685 | 22 | 27,371 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image> | instruction | 0 | 13,689 | 22 | 27,378 |
Tags: implementation, number theory
Correct Solution:
```
size,n=map(int,input().split())
count=0
for i in range(1, size+1):
if n%i==0 and n<=size*i:
count=count+1
print(count)
``` | output | 1 | 13,689 | 22 | 27,379 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image> | instruction | 0 | 13,690 | 22 | 27,380 |
Tags: implementation, number theory
Correct Solution:
```
import sys
import itertools
import math
import collections
from collections import Counter
#########################
# imgur.com/Pkt7iIf.png #
#########################
def sieve(n):
prime = [True for i in range(n + 1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * 2, n + 1, p):
prime[i] = False
p += 1
prime[0] = prime[1] = False
r = [p for p in range(n + 1) if prime[p]]
return r
def divs(n, start=1):
r = []
for i in range(start, int(math.sqrt(n) + 1)):
if (n % i == 0):
if (n / i == i):
r.append(i)
else:
r.extend([i, n // i])
return r
def ceil(n, k): return n // k + (n % k != 0)
def ii(): return int(input())
def mi(): return map(int, input().split())
def li(): return list(map(int, input().split()))
def lcm(a, b): return abs(a * b) // math.gcd(a, b)
def prr(a, sep=' '): print(sep.join(map(str, a)))
def dd(): return collections.defaultdict(int)
n, x = mi()
print(len([i for i in divs(x) if i <= n and x // i <= n]))
``` | output | 1 | 13,690 | 22 | 27,381 |
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