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Provide a correct Python 3 solution for this coding contest problem. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. ...
instruction
0
14,760
22
29,520
"Correct Solution: ``` def inv_gcd(a, b): a = (a + b) % b if a == 0: return (b, 0) s, t = b, a m0, m1 = 0, 1 while t: u = s // t s -= t * u m0 -= m1 * u tmp = s s = t t = tmp tmp = m0 m0 = m1 m1 = tmp if m0 ...
output
1
14,760
22
29,521
Provide a correct Python 3 solution for this coding contest problem. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. ...
instruction
0
14,764
22
29,528
"Correct Solution: ``` def egcd(a, b): if a == 0: return (b, 0, 1) else: g, y, x = egcd(b % a, a) return (g, x - (b // a) * y, y) def modinv(a, m): g, x, y = egcd(a, m) if g != 1: raise Exception('modular inverse does not exist') else: return x % m N = int(i...
output
1
14,764
22
29,529
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 ...
instruction
0
14,767
22
29,534
Yes
output
1
14,767
22
29,535
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 ...
instruction
0
14,768
22
29,536
Yes
output
1
14,768
22
29,537
Provide tags and a correct Python 3 solution for this coding contest problem. Input The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space. Output Output "YES" or "NO". Examples Input 2 3 Output YES Input 3 2 Output NO Input 33 16 Output YES Input ...
instruction
0
15,312
22
30,624
Tags: *special, number theory Correct Solution: ``` import sys import collections def int2base(dec, base): ans = [] while(dec > 0): ans.insert(0,dec % base) dec //= base return ans def xenodrome(num_list): most_common = collections.Counter(num_list).most_common(1) return most_co...
output
1
15,312
22
30,625
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,374
22
30,748
Tags: brute force, number theory, sortings Correct Solution: ``` n=int(input()) a=list(map(int,input().split())) m=min(a) for i in range(n): if a[i]%m!=0: print(-1) exit() print(m) ```
output
1
15,374
22
30,749
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,375
22
30,750
Tags: brute force, number theory, sortings Correct Solution: ``` a = int(input()) array = list(map(int, input().split())) array.sort() count = 0 for i in array[1:]: if i % array[0] == 0: count += 1 continue else: break if count == len(array) - 1: print(array[0]) else: print(-1) `...
output
1
15,375
22
30,751
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,376
22
30,752
Tags: brute force, number theory, sortings Correct Solution: ``` from math import * n=int(input()) l=list(map(int,input().split())) g=l[0] for i in range(1,n): g=gcd(g,l[i]) if(g in l): print(g) else: print(-1) ```
output
1
15,376
22
30,753
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,377
22
30,754
Tags: brute force, number theory, sortings Correct Solution: ``` f,n,l=0,int(input()),sorted(map(int,input().split())) for x in range(n): if l[x]%l[0]!=0:f=1;break print([l[0],-1][f==1]) ```
output
1
15,377
22
30,755
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,378
22
30,756
Tags: brute force, number theory, sortings Correct Solution: ``` n, t = int(input()), list(map(int, input().split())) k = min(t) print(-1 if any(i % k for i in t) else k) ```
output
1
15,378
22
30,757
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,379
22
30,758
Tags: brute force, number theory, sortings Correct Solution: ``` from math import gcd n = int(input()) arr = [int(x) for x in input().split()];g = arr[0] for i in arr: g = gcd(g,i) if g in arr: print(g) else: print(-1) ```
output
1
15,379
22
30,759
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,380
22
30,760
Tags: brute force, number theory, sortings Correct Solution: ``` def gcd(a, b): factor = a while b%factor != 0: temp = factor factor = b%factor b = temp return(factor) def main(): n = int(input()) arr = list(map(int, input().split(" "))) if n == 1: print(arr[0]) return factor = gcd(arr[0], arr[1]) f...
output
1
15,380
22
30,761
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by ...
instruction
0
15,381
22
30,762
Tags: brute force, number theory, sortings Correct Solution: ``` c=0; input(); l=sorted(map(int,input().split())) for i in l: if i%l[0]!=0:c=1;break print([-1,l[0]][c==0]) ```
output
1
15,381
22
30,763
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,382
22
30,764
Yes
output
1
15,382
22
30,765
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,383
22
30,766
Yes
output
1
15,383
22
30,767
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,384
22
30,768
Yes
output
1
15,384
22
30,769
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,385
22
30,770
Yes
output
1
15,385
22
30,771
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,386
22
30,772
No
output
1
15,386
22
30,773
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,387
22
30,774
No
output
1
15,387
22
30,775
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,388
22
30,776
No
output
1
15,388
22
30,777
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the a...
instruction
0
15,389
22
30,778
No
output
1
15,389
22
30,779
Provide tags and a correct Python 3 solution for this coding contest problem. It's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes ...
instruction
0
15,412
22
30,824
Tags: constructive algorithms, number theory Correct Solution: ``` #!/usr/bin/env python3 from sys import stdin MAXNUM = int(2e6) primes = list() isprime = [True for i in range(MAXNUM+1)] def getPrimes(): for i in range(2, MAXNUM+1): if isprime[i]: primes.append(i) j = i*i ...
output
1
15,412
22
30,825
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,525
22
31,050
Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys from functools import lru_cache, cmp_to_key from heapq import merge, heapify, heappop, heappush from math import ceil, floor, gcd, fabs, factorial, fmod, sqrt, inf from collections import defaultdict as dd, deque, Counter as C from iterto...
output
1
15,525
22
31,051
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,526
22
31,052
Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys def main(): a = [2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49] factors_count = 0 for i in a: print(i, flush=True) read = sys.stdin.readline().strip() if read == "yes": factors_count += 1 if factors_count > 1: break...
output
1
15,526
22
31,053
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,527
22
31,054
Tags: constructive algorithms, interactive, math Correct Solution: ``` import os import sys if os.path.exists('/mnt/c/Users/Square/square/codeforces'): f = iter(open('A.txt').readlines()) def input(): return next(f) input = lambda: sys.stdin.readline().strip() else: input = lambda: sys.stdin.readline().strip() ...
output
1
15,527
22
31,055
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,528
22
31,056
Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys input = sys.stdin.readline flush = sys.stdout.flush def query(x): print(x) flush() y = input()[:-1] return 1 if y == "yes" else 0 A = [2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49] cnt =...
output
1
15,528
22
31,057
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,529
22
31,058
Tags: constructive algorithms, interactive, math Correct Solution: ``` #------------------Important Modules------------------# from sys import stdin,stdout from bisect import bisect_left as bl from bisect import bisect_right as br from heapq import * from random import * from itertools import permutations input=stdin.r...
output
1
15,529
22
31,059
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,530
22
31,060
Tags: constructive algorithms, interactive, math Correct Solution: ``` #Code by Sounak, IIESTS #------------------------------warmup---------------------------- import os import sys import math from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file)...
output
1
15,530
22
31,061
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,531
22
31,062
Tags: constructive algorithms, interactive, math Correct Solution: ``` #------------------------template--------------------------# import os import sys from math import * from collections import * # from fractions import * # from heapq import* from bisect import * from io import BytesIO, IOBase def vsInput(): sys....
output
1
15,531
22
31,063
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is pri...
instruction
0
15,532
22
31,064
Tags: constructive algorithms, interactive, math Correct Solution: ``` import os import sys from io import BytesIO, IOBase import math from decimal import * from collections import defaultdict getcontext().prec = 25 MOD = pow(10, 9) + 7 BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, f...
output
1
15,532
22
31,065
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,533
22
31,066
Yes
output
1
15,533
22
31,067
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,534
22
31,068
Yes
output
1
15,534
22
31,069
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,535
22
31,070
Yes
output
1
15,535
22
31,071
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,536
22
31,072
Yes
output
1
15,536
22
31,073
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,537
22
31,074
No
output
1
15,537
22
31,075
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,538
22
31,076
No
output
1
15,538
22
31,077
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,539
22
31,078
No
output
1
15,539
22
31,079
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. ...
instruction
0
15,540
22
31,080
No
output
1
15,540
22
31,081
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,626
22
33,252
"Correct Solution: ``` a, b, k = map(int, input().split()) n = [] for i in range(1, 101): if a%i==0 and b%i==0: n.append(i) print(n[-k]) ```
output
1
16,626
22
33,253
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,627
22
33,254
"Correct Solution: ``` A,B,K=map(int,input().split()) List=[] for i in range (1,101): if A%i==0 and B%i==0: List.append(i) print(List[-K]) ```
output
1
16,627
22
33,255
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,628
22
33,256
"Correct Solution: ``` A, B, K = map(int, input().split()) m = [x for x in range(1, min(A, B)+1) if A%x==0 and B%x==0] print(m[-K]) ```
output
1
16,628
22
33,257
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,629
22
33,258
"Correct Solution: ``` A, B, K = map(int,input().split()) l = [x for x in range(1,A+1) if A%x == 0 and B%x == 0] print(l[-K]) ```
output
1
16,629
22
33,259
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,630
22
33,260
"Correct Solution: ``` a,b,k=[int(s) for s in input().split()] c=[] for i in range(1,101): if a%i==0 and b%i==0: c = c+[i] print(c[-k]) ```
output
1
16,630
22
33,261
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,631
22
33,262
"Correct Solution: ``` a,b,k=map(int,input().split()) list = [] for i in range(1,min(a,b)+1): if(a%i==0 and b%i==0): list.append(i) print(list[-k]) ```
output
1
16,631
22
33,263
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,632
22
33,264
"Correct Solution: ``` a,b,k=map(int,input().split()) print(list(filter(lambda x:a%x+b%x==0, [i for i in range(min(a,b),0,-1)]))[k-1]) ```
output
1
16,632
22
33,265
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th lar...
instruction
0
16,633
22
33,266
"Correct Solution: ``` a,b,k=map(int,input().split()) l=[] for i in range(min(a,b),0,-1): if a%i==b%i==0: l.append(i) print(l[k-1]) ```
output
1
16,633
22
33,267
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in i...
instruction
0
16,634
22
33,268
Yes
output
1
16,634
22
33,269
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in i...
instruction
0
16,635
22
33,270
Yes
output
1
16,635
22
33,271
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in i...
instruction
0
16,636
22
33,272
Yes
output
1
16,636
22
33,273
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in i...
instruction
0
16,637
22
33,274
Yes
output
1
16,637
22
33,275