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.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,242 | 22 | 34,484 |
Tags: dp, math
Correct Solution:
```
s, x = map(int, input().split(' '))
if (s-x)%2 or s < x:
print(0)
else:
c = bin((s-x)//2)[2:][::-1]
t = bin(x)[2:][::-1]
for i in range(len(t)):
if t[i] == '1' and i < len(c) and c[i] == '1':
print(0)
exit(0)
print(pow(2, bin(x)[2:... | output | 1 | 17,242 | 22 | 34,485 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,243 | 22 | 34,486 |
Tags: dp, math
Correct Solution:
```
import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop
from bisect import bisect_left , bisect_right
import math
alphabets = list('abcdefghijklmnopqrstuvwxyz')
def isPrime(x)... | output | 1 | 17,243 | 22 | 34,487 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,244 | 22 | 34,488 |
Tags: dp, math
Correct Solution:
```
a, b = [int(x) for x in input().split()]
c = (a-b) / 2
if c < 0 or not c.is_integer() or int(c) & b:
print(0)
exit(0)
t = 0
while b:
t += b & 1
b >>= 1
t = 1 << t
if c == 0:
t -= 2
print(t)
``` | output | 1 | 17,244 | 22 | 34,489 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,245 | 22 | 34,490 |
Tags: dp, math
Correct Solution:
```
'''
___ ____
____ _____ _____/ (_)_ ______ ____ _____/ / /_ __ ______ ___ __
/ __ `/ __ `/ __ / / / / / __ \/ __ `/ __ / __ \/ / / / __ `/ / / /
/ /_/ / /_/ / /_/ / / /_/ / /_/ / /_/ / /_/ / / / / /_/ / /_/ / /_/ /... | output | 1 | 17,245 | 22 | 34,491 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,246 | 22 | 34,492 |
Tags: dp, math
Correct Solution:
```
s, x = map(int, input().split())
print(0 if s < x or (s - x) & (2 * x + 1) else 2 ** bin(x).count('1') - 2 * (s == x))
# Made By Mostafa_Khaled
``` | output | 1 | 17,246 | 22 | 34,493 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,247 | 22 | 34,494 |
Tags: dp, math
Correct Solution:
```
suma,xor=map(int,input().split())
mitad=round((suma-xor)/2)
if(mitad<0 or mitad*2+xor!=suma or (mitad&xor)!=0):
print(0)
else:
print(2**(bin(xor).count("1"))-2*(suma==xor))
``` | output | 1 | 17,247 | 22 | 34,495 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,248 | 22 | 34,496 |
Tags: dp, math
Correct Solution:
```
s, xx = map(int, input().split())
if s - xx & 1 or s < xx:
exit(print(0))
y = bin(s - xx)[2:-1]
x = bin(xx)[2:]
ans = 1
if len(y) < len(x):
y = '0' * (len(x) - len(y)) + y
else:
x = '0' * (len(y) - len(x)) + x
for i in range(len(x)):
if x[i] == '1' and y[i] == '1':
... | output | 1 | 17,248 | 22 | 34,497 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
Input
The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and... | instruction | 0 | 17,249 | 22 | 34,498 |
Tags: dp, math
Correct Solution:
```
s, x = map(int, input().split())
a, b = 1, 0
for i in range(50):
c, d = s & (1 << i), x & (1 << i)
# print(i, a, b, c, d)
if c == d:
if c:
a, b = 2 * a, 0
else:
a, b = a, a
else:
if c:
a, b = b, b
el... | output | 1 | 17,249 | 22 | 34,499 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,352 | 22 | 34,704 |
Tags: brute force, constructive algorithms
Correct Solution:
```
from random import randint
h = [-1] * 2000001
for t in range(int(input())):
n, A = int(input()), list(map(int, input().split()))
B = []
while len(B) < n:
b = randint(1, 1000000)
if all(h[a + b] != t for a in A):
for... | output | 1 | 17,352 | 22 | 34,705 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,353 | 22 | 34,706 |
Tags: brute force, constructive algorithms
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
a=list(map(int, input().split()))
a.sort()
b=[]
b.append(1)
t=10**6
used=[0]*(t+1)
used[1]=1
can_be=2
diffs=[]
for i in range(n):
for j in range(i+1,n):
... | output | 1 | 17,353 | 22 | 34,707 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,354 | 22 | 34,708 |
Tags: brute force, constructive algorithms
Correct Solution:
```
from collections import defaultdict, deque, Counter
from sys import stdin, stdout
from heapq import heappush, heappop
import math
import io
import os
import math
import bisect
#?############################################################
def isPrime(x... | output | 1 | 17,354 | 22 | 34,709 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,355 | 22 | 34,710 |
Tags: brute force, constructive algorithms
Correct Solution:
```
visited = [-1] * (2 * 10 ** 6 + 1)
t = int(input())
for i in range(t):
n, A = int(input()), list(map(int, input().split()))
A.sort()
res = []
v = 1
while len(res) < n:
flag = True
for a in A:
if visited[a + ... | output | 1 | 17,355 | 22 | 34,711 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,356 | 22 | 34,712 |
Tags: brute force, constructive algorithms
Correct Solution:
```
from random import randint
visited = [-1] * (2 * 10 ** 6 + 1)
t = int(input())
for i in range(t):
n, A = int(input()), list(map(int, input().split()))
res = []
while len(res) < n:
v = randint(1, 10**6)
flag = True
for ... | output | 1 | 17,356 | 22 | 34,713 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,357 | 22 | 34,714 |
Tags: brute force, constructive algorithms
Correct Solution:
```
from random import randint
def solve():
n, aa = int(input()), list(map(int, input().split()))
bb, ab = set(), set()
while True:
b = randint(1, 1000000)
for a in aa:
if a + b in ab:
break
el... | output | 1 | 17,357 | 22 | 34,715 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,358 | 22 | 34,716 |
Tags: brute force, constructive algorithms
Correct Solution:
```
d = [-1] * 1000001
for t in range(int(input())):
n, a = int(input()), list(map(int, input().split()))
a.sort()
for i in range(n):
for j in range(i + 1, n): d[a[j] - a[i]] = t
i = 1
while any(d[i * j] == t for j in range(1, n))... | output | 1 | 17,358 | 22 | 34,717 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers ai on a blackboard. Now he asks Masha to create a set B containing n different integers bj such that all n2 integer... | instruction | 0 | 17,359 | 22 | 34,718 |
Tags: brute force, constructive algorithms
Correct Solution:
```
from random import randint
visited = [-1] * (2 * 10 ** 6 + 1)
t = int(input())
for i in range(t):
n, A = int(input()), list(map(int, input().split()))
res = []
while len(res) < n:
v = randint(1, 10**6)
if all(visited[a + v] !=... | output | 1 | 17,359 | 22 | 34,719 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,677 | 22 | 35,354 |
"Correct Solution:
```
a,b=input().split(" ")
a=int(a)
b=int(b)
print(a%b)
``` | output | 1 | 17,677 | 22 | 35,355 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,678 | 22 | 35,356 |
"Correct Solution:
```
if __name__ == "__main__":
a, b = list(map(lambda x: int(x), input().split()))
print(a % b)
``` | output | 1 | 17,678 | 22 | 35,357 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,679 | 22 | 35,358 |
"Correct Solution:
```
def main():
a,b = map(int, input().split())
print(a%b)
main()
``` | output | 1 | 17,679 | 22 | 35,359 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,680 | 22 | 35,360 |
"Correct Solution:
```
a, b = input().split()
print(int(a) % int(b))
``` | output | 1 | 17,680 | 22 | 35,361 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,681 | 22 | 35,362 |
"Correct Solution:
```
a, b=input().split(' ')
a=int(a)
b=int(b)
print(a-a//b*b)
``` | output | 1 | 17,681 | 22 | 35,363 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,682 | 22 | 35,364 |
"Correct Solution:
```
print(eval(input().replace(" ","%")))
``` | output | 1 | 17,682 | 22 | 35,365 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,683 | 22 | 35,366 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Big Integers - Remainder of Big Integers
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=NTL_2_E&lang=jp
"""
import sys
def main(args):
A, B = map(int, input().split())
print(A % B)
if __name__ == '__main__':
main(sys.argv[1:])
``` | output | 1 | 17,683 | 22 | 35,367 |
Provide a correct Python 3 solution for this coding contest problem.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the remainder in a line.
Constraints
* $0 \leq A,... | instruction | 0 | 17,684 | 22 | 35,368 |
"Correct Solution:
```
A,B = map(int,input().split())
print(A % B)
``` | output | 1 | 17,684 | 22 | 35,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Remainder of Big Integers
Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
P... | instruction | 0 | 17,688 | 22 | 35,376 |
Yes | output | 1 | 17,688 | 22 | 35,377 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,763 | 22 | 35,526 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
p=10**9+7
import math
def r(l):
x=1
for m in l:
x=x*m%p
return x
n=int(input())
a,k,x,t=[],int(math.log2(n)),n,0
while x>0:
a.append(x-x//2)
x//=2
b=[n//(3*2**i)-n//(6*2**i) for i in range(k+1)]
d=[n//2**i-n//(3*2**i) for i i... | output | 1 | 17,763 | 22 | 35,527 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,764 | 22 | 35,528 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
p=10**9+7
import math
def inv(k,p):
prod=1
while k>1:
prod*=(p//k+1)
k=(k*(p//k+1))%p
return prod%p
n=int(input())
a=[]
k=int(math.log2(n))
x=n
while x>0:
y=x//2
a.append(x-y)
x=y
c=[sum(a[i:]) for i in range(k+1)... | output | 1 | 17,764 | 22 | 35,529 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,765 | 22 | 35,530 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
import math
p=10**9+7
n=int(input())
k=int(math.log2(n))
f=[[n//(2**i*3**j) for j in range(3)] for i in range(k+1)]
old=[[0,0,0] for i in range(k+1)]
old[k][0]=1
if n>=3*2**(k-1):
old[k-1][1]=1
m=n//2+2
for i in range(2,m):
dp=[[0,0,0] for i in ... | output | 1 | 17,765 | 22 | 35,531 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,766 | 22 | 35,532 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
p=10**9+7
import math
def prod(l):
x=1
for m in l:
x*=m
return x
n=int(input())
a=[]
k=int(math.log2(n))
x=n
while x>0:
y=x//2
a.append(x-y)
x=y
c=[sum(a[i:]) for i in range(k+1)]
b=[n//(3*2**i)-n//(6*2**i) for i in range... | output | 1 | 17,766 | 22 | 35,533 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,767 | 22 | 35,534 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
p=10**9+7
import math
def r(l):
x=1
for m in l:
x=x*m%p
return x
n=int(input())
a,k,x,t=[],int(math.log2(n)),n,0
while x>0:
a.append(x-x//2)
x//=2
b=[n//(3*2**i)-n//(6*2**i) for i in range(k+1)]
d=[n//2**i-n//(3*2**i) for i i... | output | 1 | 17,767 | 22 | 35,535 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,768 | 22 | 35,536 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
def perm(a,b):
ret = 1
for i in range(a, a - b, -1):
ret = (ret * i)%1000000007
return ret
num = int(input())
num2 = num
c = 0
while num2:
c += 1
num2 >>= 1
pow2 = 1 << (c-1)
array = [pow2]
for i in range(c-1):
array.app... | output | 1 | 17,768 | 22 | 35,537 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of ... | instruction | 0 | 17,769 | 22 | 35,538 |
Tags: combinatorics, dp, math, number theory
Correct Solution:
```
p=10**9+7
import math
def prod(l):
x=1
for m in l:
x=x*m%p
return x
n=int(input())
a,k,x,t=[],int(math.log2(n)),n,0
while x>0:
a.append(x-x//2)
x//=2
c=[sum(a[i:]) for i in range(k+1)]
b=[n//(3*2**i)-n//(6*2**i) for i in rang... | output | 1 | 17,769 | 22 | 35,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (... | instruction | 0 | 17,770 | 22 | 35,540 |
No | output | 1 | 17,770 | 22 | 35,541 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (... | instruction | 0 | 17,771 | 22 | 35,542 |
No | output | 1 | 17,771 | 22 | 35,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (... | instruction | 0 | 17,772 | 22 | 35,544 |
No | output | 1 | 17,772 | 22 | 35,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (... | instruction | 0 | 17,773 | 22 | 35,546 |
No | output | 1 | 17,773 | 22 | 35,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,811 | 22 | 35,622 |
Tags: math, number theory
Correct Solution:
```
from math import gcd
# from operator import mul
# from collections import defaultdict
# from itertools import count
# from functools import reduce
# primes_cache, prime_jumps = [], defaultdict(list)
# def primes():
# prime = 1
# for i in count():
# if i < ... | output | 1 | 17,811 | 22 | 35,623 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,812 | 22 | 35,624 |
Tags: math, number theory
Correct Solution:
```
from math import gcd
def Fenjie(n):
k = {}
if (n == 1):
return {}
a = 2
while (n >= 2):
if (a*a > n):
if (n in k):
k[n] += 1
else:
k[n] = 1
break
b = n%a
i... | output | 1 | 17,812 | 22 | 35,625 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,813 | 22 | 35,626 |
Tags: math, number theory
Correct Solution:
```
import sys, math
for ii in range(int(input())):
a,m = map(int,input().split())
g = math.gcd(a,m)
m=int(m/g)
ans = m
for i in range(2,int(math.sqrt(m))+1):
if m%i==0:
ans-=(ans/i)
while m%i==0:
m=int(m/i)
if ... | output | 1 | 17,813 | 22 | 35,627 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,814 | 22 | 35,628 |
Tags: math, number theory
Correct Solution:
```
primes=[True]*1000001
primes[0]=False
primes[1]=False
for i in range(2, 100001):
if primes[i]:
for j in range(i*2, 100001, i):
primes[j]=False
pL=[]
for i in range(2, 100001):
if primes[i]:pL.append(i)
def fact(n):
L=[]
for i in pL:
... | output | 1 | 17,814 | 22 | 35,629 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,815 | 22 | 35,630 |
Tags: math, number theory
Correct Solution:
```
from math import gcd
def phi(n) :
res=n
p=2
while(p*p<=n):
if(n%p==0):
while(n%p==0) :
n//=p
res//=p
res*=(p-1)
p+=1
if(n>1):
res//=n
res*=(n-1)
return(res)
t=int(inp... | output | 1 | 17,815 | 22 | 35,631 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,816 | 22 | 35,632 |
Tags: math, number theory
Correct Solution:
```
import sys
input = sys.stdin.readline
import math
t=int(input())
for test in range(t):
a,m=map(int,input().split())
GCD=math.gcd(a,m)
x=m//GCD
L=int(math.sqrt(x))
FACT=dict()
for i in range(2,L+2):
while x%i==0:
FACT[i]=FACT.... | output | 1 | 17,816 | 22 | 35,633 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,817 | 22 | 35,634 |
Tags: math, number theory
Correct Solution:
```
import math
def Phi_Euler(val) :
ans = val
i = 2
while i*i <= val :
if val%i == 0 :
ans -= ans//i
while val%i == 0 : val //= i
i += 1
if val > 1 : ans -= ans//val
return ans
t = int(input())
while t > 0 :
... | output | 1 | 17,817 | 22 | 35,635 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
The first line contains the single integer T (1 ... | instruction | 0 | 17,818 | 22 | 35,636 |
Tags: math, number theory
Correct Solution:
```
def gcd(x,y):
while(y):
x,y=y,x%y
return x
def totient(x):
tot=x
n=x
i=1
prime_factors=[]
q=2
while n>1 and q*q<=n:
if n%q==0:
prime_factors.append(q)
while(n%q==0):
n//=q
q+=1
if n>1:
prime_factors.append(n)
for p in prime_factors:
... | output | 1 | 17,818 | 22 | 35,637 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,819 | 22 | 35,638 |
Yes | output | 1 | 17,819 | 22 | 35,639 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,820 | 22 | 35,640 |
Yes | output | 1 | 17,820 | 22 | 35,641 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,821 | 22 | 35,642 |
Yes | output | 1 | 17,821 | 22 | 35,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,822 | 22 | 35,644 |
Yes | output | 1 | 17,822 | 22 | 35,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,823 | 22 | 35,646 |
No | output | 1 | 17,823 | 22 | 35,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).
Note: \gcd(a, b) is the greatest common divisor of a and b.
Input
T... | instruction | 0 | 17,824 | 22 | 35,648 |
No | output | 1 | 17,824 | 22 | 35,649 |
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