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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