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.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input
The first line contains integers n, p, k (2 ≤... | instruction | 0 | 1,731 | 22 | 3,462 |
Tags: math, matrices, number theory, two pointers
Correct Solution:
```
from collections import Counter
def pr(a):return (a*(a-1))//2
n,p,k=map(int,input().split())
a=map(int,input().split())
a=Counter([(x**4-x*k+p)%p for x in a])
print(sum(pr(a[x]) for x in a))
``` | output | 1 | 1,731 | 22 | 3,463 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input
The first line contains integers n, p, k (2 ≤... | instruction | 0 | 1,732 | 22 | 3,464 |
Tags: math, matrices, number theory, two pointers
Correct Solution:
```
from sys import stdin
n,p,k=map(int,stdin.readline().strip().split())
s=list(map(int,stdin.readline().strip().split()))
st=set()
d=dict()
for i in s:
x=(i**4-i*k)%p
if x in st:
d[x]+=1
else:
st.add(x)
d[x]=1
s.so... | output | 1 | 1,732 | 22 | 3,465 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input
The first line contains integers n, p, k (2 ≤... | instruction | 0 | 1,733 | 22 | 3,466 |
Tags: math, matrices, number theory, two pointers
Correct Solution:
```
n,p,k=map(int,input().split())
arr=list(map(int,input().split()))
dict1={}
for i in range(n):
val=((pow(arr[i],4,p)-(k*arr[i])%p)+p)%p
try:
dict1[val]+=1
except:
KeyError
dict1[val]=1
ans=0
for i in dict1.keys():
ans+=(dict1[i]*(dict1[i]... | output | 1 | 1,733 | 22 | 3,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,734 | 22 | 3,468 |
Yes | output | 1 | 1,734 | 22 | 3,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,735 | 22 | 3,470 |
Yes | output | 1 | 1,735 | 22 | 3,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,736 | 22 | 3,472 |
Yes | output | 1 | 1,736 | 22 | 3,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,737 | 22 | 3,474 |
Yes | output | 1 | 1,737 | 22 | 3,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,738 | 22 | 3,476 |
No | output | 1 | 1,738 | 22 | 3,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,739 | 22 | 3,478 |
No | output | 1 | 1,739 | 22 | 3,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,740 | 22 | 3,480 |
No | output | 1 | 1,740 | 22 | 3,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a prime number p, n integers a_1, a_2, …, a_n, and an integer k.
Find the number of pairs of indexes (i, j) (1 ≤ i < j ≤ n) for which (a_i + a_j)(a_i^2 + a_j^2) ≡ k mod p.
Input... | instruction | 0 | 1,741 | 22 | 3,482 |
No | output | 1 | 1,741 | 22 | 3,483 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,758 | 22 | 3,516 |
Tags: hashing, math, number theory
Correct Solution:
```
import sys
input=sys.stdin.readline
from collections import defaultdict
n,k=map(int,input().split())
a=list(map(int,input().split()))
dd=defaultdict(int)
ans=0
for aa in a:
primes=[]
b=aa
for j in range(2,int(b**0.5)+1):
if b%j==0:
... | output | 1 | 1,758 | 22 | 3,517 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,759 | 22 | 3,518 |
Tags: hashing, math, number theory
Correct Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
d = {}
ans = 0
for el in a:
i = 2
a = []
b = []
while i*i <= el:
cnt = 0
while not(el%i):
el //= i
cnt += 1
if cnt%k:
... | output | 1 | 1,759 | 22 | 3,519 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,760 | 22 | 3,520 |
Tags: hashing, math, number theory
Correct Solution:
```
from collections import defaultdict
# The largest prime of that divides i where 2 <= i <= N
largerPrime = list(range(10**5+1))
def largestPrime(N = 10**5):
#[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,... | output | 1 | 1,760 | 22 | 3,521 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,761 | 22 | 3,522 |
Tags: hashing, math, number theory
Correct Solution:
```
from collections import defaultdict
n, k = map(int, input().split())
a = list(map(int, input().split()))
n = int(max(a)**.5)
mark = [True]*(n+1)
primes = []
for i in range(2,n+1):
if mark[i]:
primes.append(i)
for j in range(i, n+1, i): mark[j] = False
d = ... | output | 1 | 1,761 | 22 | 3,523 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,762 | 22 | 3,524 |
Tags: hashing, math, number theory
Correct Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 2/11/20
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
import math
def factors(val):
wc = []
for i in range(2, int(math.sqrt(val)) ... | output | 1 | 1,762 | 22 | 3,525 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,763 | 22 | 3,526 |
Tags: hashing, math, number theory
Correct Solution:
```
import math as mt
from typing import Counter
# Calculando SPF (Smallest Prime Factor)
# para todo número hasta MAXN.
def sieve():
spf[1] = 1
for i in range(2, MAXN):
# Marcando como SPF de cada número
# para que sea el mismo
spf[i... | output | 1 | 1,763 | 22 | 3,527 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,764 | 22 | 3,528 |
Tags: hashing, math, number theory
Correct Solution:
```
from math import sqrt
def gd(n, k):
ans = 1
obrans = 1
for i in range(2, int(sqrt(n) + 1)):
j = 0
while n % i == 0:
j += 1
n //= i
ans *= pow(i, j%k)
obrans *= pow(i, (-j)%k)
ans *= n
obr... | output | 1 | 1,764 | 22 | 3,529 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The first line contains two integers n and k (2 ≤ n... | instruction | 0 | 1,765 | 22 | 3,530 |
Tags: hashing, math, number theory
Correct Solution:
```
n, k = map(int, input().split())
arr = list(map(int, input().split()))
ans = 0
d = {}
for i in range(n):
x = 2
a = []
b = []
y = arr[i]
while x * x <= arr[i]:
if arr[i] % x == 0:
c = 0
while y % x == 0:
... | output | 1 | 1,765 | 22 | 3,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The ... | instruction | 0 | 1,768 | 22 | 3,536 |
Yes | output | 1 | 1,768 | 22 | 3,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The ... | instruction | 0 | 1,769 | 22 | 3,538 |
Yes | output | 1 | 1,769 | 22 | 3,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.
Input
The ... | instruction | 0 | 1,770 | 22 | 3,540 |
No | output | 1 | 1,770 | 22 | 3,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Bizon the Champion isn't just friendly, he also is a rigorous coder.
Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divisors of a1 go in the increasing order, then all ... | instruction | 0 | 1,982 | 22 | 3,964 |
Tags: brute force, dfs and similar, implementation, number theory
Correct Solution:
```
import sys
solSaved = {}
solSavedPropios = {}
def DivisorsN(n):
key = solSaved.get(str(n))
if key == None :
divisors = []
divisors2 = []
for i in range(1,int(n ** (1/2)) + 1):
if n % ... | output | 1 | 1,982 | 22 | 3,965 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bizon the Champion isn't just friendly, he also is a rigorous coder.
Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divis... | instruction | 0 | 1,983 | 22 | 3,966 |
No | output | 1 | 1,983 | 22 | 3,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bizon the Champion isn't just friendly, he also is a rigorous coder.
Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divis... | instruction | 0 | 1,984 | 22 | 3,968 |
No | output | 1 | 1,984 | 22 | 3,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bizon the Champion isn't just friendly, he also is a rigorous coder.
Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divis... | instruction | 0 | 1,985 | 22 | 3,970 |
No | output | 1 | 1,985 | 22 | 3,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bizon the Champion isn't just friendly, he also is a rigorous coder.
Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divis... | instruction | 0 | 1,986 | 22 | 3,972 |
No | output | 1 | 1,986 | 22 | 3,973 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the easy version of the problem. The only difference is that in this version k = 0.
There is an array a_1, a_2, …, a_n of n positive integers. You should divide it into a minimal number of continuous segments, such that in each segm... | instruction | 0 | 2,654 | 22 | 5,308 |
Tags: data structures, dp, greedy, math, number theory, two pointers
Correct Solution:
```
import os,io,math;input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
prime=[1]*10000;prime2=[];curr=2
for i in range(2,10000):
if prime[i]:
for j in range(2*i,10000,i): prime[j]=0
prime2 = [(curr*curr) for... | output | 1 | 2,654 | 22 | 5,309 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the easy version of the problem. The only difference is that in this version k = 0.
There is an array a_1, a_2, …, a_n of n positive integers. You should divide it into a minimal number of continuous segments, such that in each segm... | instruction | 0 | 2,659 | 22 | 5,318 |
Tags: data structures, dp, greedy, math, number theory, two pointers
Correct Solution:
```
import os,io,math;input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
prime=[1]*10000;prime2=[];curr=2
for i in range(2,10000):
if prime[i]:
for j in range(2*i,10000,i): prime[j]=0
for curr in range(2,math... | output | 1 | 2,659 | 22 | 5,319 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the easy version of the problem. The only difference is that in this version k = 0.
There is an array a_1, a_2, …, a_n of n positive integers. You should divide it into a minimal number... | instruction | 0 | 2,662 | 22 | 5,324 |
Yes | output | 1 | 2,662 | 22 | 5,325 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the easy version of the problem. The only difference is that in this version k = 0.
There is an array a_1, a_2, …, a_n of n positive integers. You should divide it into a minimal number... | instruction | 0 | 2,665 | 22 | 5,330 |
Yes | output | 1 | 2,665 | 22 | 5,331 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).
You are given an array a of n... | instruction | 0 | 3,053 | 22 | 6,106 |
No | output | 1 | 3,053 | 22 | 6,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).
You are given an array a of n... | instruction | 0 | 3,054 | 22 | 6,108 |
No | output | 1 | 3,054 | 22 | 6,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).
You are given an array a of n... | instruction | 0 | 3,055 | 22 | 6,110 |
No | output | 1 | 3,055 | 22 | 6,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).
You are given an array a of n... | instruction | 0 | 3,056 | 22 | 6,112 |
No | output | 1 | 3,056 | 22 | 6,113 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by spa... | instruction | 0 | 3,363 | 22 | 6,726 |
Tags: dp, graphs, number theory, shortest paths
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
_print = print
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in... | output | 1 | 3,363 | 22 | 6,727 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by spa... | instruction | 0 | 3,364 | 22 | 6,728 |
Tags: dp, graphs, number theory, shortest paths
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
_print = print
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in... | output | 1 | 3,364 | 22 | 6,729 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by spa... | instruction | 0 | 3,365 | 22 | 6,730 |
Tags: dp, graphs, number theory, shortest paths
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
_print = print
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in... | output | 1 | 3,365 | 22 | 6,731 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and... | instruction | 0 | 3,366 | 22 | 6,732 |
No | output | 1 | 3,366 | 22 | 6,733 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and... | instruction | 0 | 3,367 | 22 | 6,734 |
No | output | 1 | 3,367 | 22 | 6,735 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and... | instruction | 0 | 3,368 | 22 | 6,736 |
No | output | 1 | 3,368 | 22 | 6,737 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and... | instruction | 0 | 3,369 | 22 | 6,738 |
No | output | 1 | 3,369 | 22 | 6,739 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,376 | 22 | 6,752 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
from collections import defaultdict
import math
def ncr(n,m):
return math.factorial(n)//((math.factorial(m)*math.factorial(n-m)))
def gcd(n,m):
return math.gcd(n,m)
power=[]
def cal():
temp=1
power.append(temp)
for i in range(2,... | output | 1 | 3,376 | 22 | 6,753 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,377 | 22 | 6,754 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math
def ans2(n):
if n==0:
return 1
res = 2**(math.floor(math.log2(n))+1)-1
if res == n:
lst = [1,1,1,5,1,21,1,85,73,341,89,1365,1,5461,4681,21845,1,87381,1,349525,299593,1398101,178481,5592405,1082401]
res = lst[math.ceil(math.log... | output | 1 | 3,377 | 22 | 6,755 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,378 | 22 | 6,756 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math
def factors(num):
ans = 1
n = int(math.sqrt(num)) + 1
for i in range(1, n):
if num % i == 0:
a1 = num // i
a2 = i
if a1 < num:
if a1 > ans:
a... | output | 1 | 3,378 | 22 | 6,757 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,379 | 22 | 6,758 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
from math import *
q=int(input())
ansarr=[]
for l in range(q):
n=int(input())
b1=bin(n)[2:]
if(b1.count('1')==len(b1)):
flag=0
for i in range(2,ceil(sqrt(n))):
if(n%i==0):
ansarr.append(n//i)
flag=1
break
if(flag==0):
an... | output | 1 | 3,379 | 22 | 6,759 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,380 | 22 | 6,760 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math
def f(p):
L = []
for i in range(1,int(math.sqrt(p))+1):
if p % i == 0:
L.append(i)
if i != p//i:
L.append(p//i)
L.sort()
return L[-2]
R = lambda: map(int, input().split()... | output | 1 | 3,380 | 22 | 6,761 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,381 | 22 | 6,762 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math
def isPowerOfTwo (x):
# First x in the below expression
# is for the case when x is 0
return (x and (not(x & (x - 1))) )
def main():
t = int(input())
while t > 0:
t -= 1
n = int(input())
... | output | 1 | 3,381 | 22 | 6,763 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,382 | 22 | 6,764 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
from math import log
q = int(input())
for i in range(q):
w = int(input())
if log(w+1,2)>int(log(w+1,2)):
print(2**(int(log(w+1,2))+1)-1)
else:
c = w
p = 3
k = False
while k == False and p<=int(w*... | output | 1 | 3,382 | 22 | 6,765 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that t... | instruction | 0 | 3,383 | 22 | 6,766 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
from math import gcd, sqrt, ceil
def check_pow2(a):
return 2 ** a.bit_length() == a + 1
def max_div(a):
for i in range(2, ceil(sqrt(a))+1):
if a % i == 0:
return max(i, a // i)
return 1
def solve_dumb(a):
mv ... | output | 1 | 3,383 | 22 | 6,767 |
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