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Provide tags and a correct Python 3 solution for this coding contest problem. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors greater than 1. * Subtract 1 from n if n is ...
instruction
0
76,871
19
153,742
Tags: games, math, number theory Correct Solution: ``` t=int(input()) for _ in range(t): n=int (input()) if n==2: print ('Ashishgup') continue if n==1: print ('FastestFinger') continue elif n&1: print ('Ashishgup') continue elif n%2==0: if (n//...
output
1
76,871
19
153,743
Provide tags and a correct Python 3 solution for this coding contest problem. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors greater than 1. * Subtract 1 from n if n is ...
instruction
0
76,872
19
153,744
Tags: games, math, number theory Correct Solution: ``` def primo(k): if k == 1: return False i = 3 while i*i <= k: if k % i == 0: return False i += 1 return True t = int(input()) for test in range(t): n = int(input()) if n == 1: print("FastestFing...
output
1
76,872
19
153,745
Provide tags and a correct Python 3 solution for this coding contest problem. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors greater than 1. * Subtract 1 from n if n is ...
instruction
0
76,873
19
153,746
Tags: games, math, number theory Correct Solution: ``` for s in[*open(0)][1:]:n=int(s);print(('FastestFinger','Ashishgup')[n==2or(n&-n<n)&(n&1|any(n//2%i<1for i in range(2,int(n**.5)+1)))]) ```
output
1
76,873
19
153,747
Provide tags and a correct Python 3 solution for this coding contest problem. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors greater than 1. * Subtract 1 from n if n is ...
instruction
0
76,874
19
153,748
Tags: games, math, number theory Correct Solution: ``` import sys input = sys.stdin.readline from collections import * def factorize(n): fct = [] for i in range(2, int(n**0.5)+1): c = 0 while n%i==0: n //= i c += 1 if c>0: f...
output
1
76,874
19
153,749
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,875
19
153,750
Yes
output
1
76,875
19
153,751
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,876
19
153,752
Yes
output
1
76,876
19
153,753
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,877
19
153,754
Yes
output
1
76,877
19
153,755
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,878
19
153,756
Yes
output
1
76,878
19
153,757
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,879
19
153,758
No
output
1
76,879
19
153,759
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,880
19
153,760
No
output
1
76,880
19
153,761
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,881
19
153,762
No
output
1
76,881
19
153,763
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ashishgup and FastestFinger play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: * Divide n by any of its odd divisors ...
instruction
0
76,882
19
153,764
No
output
1
76,882
19
153,765
Provide tags and a correct Python 3 solution for this coding contest problem. zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initially, the deck is shuffled uniformly randomly a...
instruction
0
76,883
19
153,766
Tags: combinatorics, dp, math, probabilities Correct Solution: ``` import sys import math Q = 998244353 n, m = list(map(int, sys.stdin.readline().strip().split())) z = [1, 1] f = [1, 1] for i in range (0, n): f[0] = f[0] * (n - i) % Q f[1] = f[1] * (n + m - i) % Q z = [(z[0]*f[1]+z[1]*f[0]) % Q, (z[1]*f[1...
output
1
76,883
19
153,767
Provide tags and a correct Python 3 solution for this coding contest problem. zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initially, the deck is shuffled uniformly randomly a...
instruction
0
76,884
19
153,768
Tags: combinatorics, dp, math, probabilities Correct Solution: ``` def modInverse(a, m) : m0 = m; y = 0; x = 1 if (m == 1): return 0 while (a > 1): q = a // m; t = m; m = a % m; a = t; t = y; y = x - q * y; x = t if (x < 0): x = x + m0 return x prime = 998244353 n, m = map(int, input().sp...
output
1
76,884
19
153,769
Provide tags and a correct Python 3 solution for this coding contest problem. zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initially, the deck is shuffled uniformly randomly a...
instruction
0
76,885
19
153,770
Tags: combinatorics, dp, math, probabilities Correct Solution: ``` # modular inverse for positive a and b and nCk mod MOD depending on modinv 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(...
output
1
76,885
19
153,771
Provide tags and a correct Python 3 solution for this coding contest problem. zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initially, the deck is shuffled uniformly randomly a...
instruction
0
76,886
19
153,772
Tags: combinatorics, dp, math, probabilities Correct Solution: ``` def b(a,m): m0=m;y=0;x=1 if (m==1):return 0 while (a>1): q=a//m;t=m;m=a%m;a=t;t=y;y=x-q*y;x=t if (x<0):x=x+m0 return x p=998244353 n,m=map(int,input().split()) z=0 for i in range(1,n+1): z+=b(i, p) print(((1+m*z)*(1+n*b(m+1...
output
1
76,886
19
153,773
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initi...
instruction
0
76,887
19
153,774
No
output
1
76,887
19
153,775
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,159
19
154,318
Yes
output
1
77,159
19
154,319
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,160
19
154,320
Yes
output
1
77,160
19
154,321
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,161
19
154,322
Yes
output
1
77,161
19
154,323
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,162
19
154,324
Yes
output
1
77,162
19
154,325
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,163
19
154,326
No
output
1
77,163
19
154,327
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,164
19
154,328
No
output
1
77,164
19
154,329
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,165
19
154,330
No
output
1
77,165
19
154,331
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the com...
instruction
0
77,166
19
154,332
No
output
1
77,166
19
154,333
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,237
19
154,474
Tags: implementation Correct Solution: ``` s = list(map(int,input().split())) cups = s[0] swapping = s[2] l = [] for i in range(cups): l.append(False) holes = list(map(int,input().split())) p = True for i in holes: if i == 1: p = False break l[i-1] = True aux = 1 for i in range(swapping): if p: swap...
output
1
77,237
19
154,475
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,238
19
154,476
Tags: implementation Correct Solution: ``` import math import random def main(n,arr,holes): if 1 in holes: return 1 bone_pos=1 for i in range(len(arr)): j,k=arr[i] if j==bone_pos: if k in holes: return k else: ...
output
1
77,238
19
154,477
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,239
19
154,478
Tags: implementation Correct Solution: ``` from sys import stdin import re def main(): l = list(map(int, filter(None, re.split(r'\W', stdin.read())))) n, m, k = l[:3] mm = [False] * (n + 1) for x in l[3:3 + m]: mm[x] = True x = 1 for u, v in zip(l[3 + m::2], l[4 + m::2]): if mm...
output
1
77,239
19
154,479
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,240
19
154,480
Tags: implementation Correct Solution: ``` if __name__ == "__main__": n,m,k = map(int,input().split()) holes = {int(i):0 for i in input().split()} poss = [False]*(n+1) poss[1] = True ans = 1 if 1 in holes: ans = 1 else: for i in range(k): x,y = map(int,input().sp...
output
1
77,240
19
154,481
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,241
19
154,482
Tags: implementation Correct Solution: ``` n, m, k = [int(x) for x in input().split()] holes = set([int(x) for x in input().split()]) now = 1 if(now in holes): print(1) exit(0) for t in range(k): i, j = [int (x) for x in input().split()] if(i == now): now = j elif(j == now): now = i if now in ho...
output
1
77,241
19
154,483
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,242
19
154,484
Tags: implementation Correct Solution: ``` n,m,k=map(int,input().split()) l=set(map(int,input().split())) i=1 for _ in range(k): u,v=map(int,input().split()) if i in l: break if i==u: i=v elif i==v: i=u print(i) # Made By Mostafa_Khaled ```
output
1
77,242
19
154,485
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,243
19
154,486
Tags: implementation Correct Solution: ``` def solve(): res = 1 n,m,k = map(int,input().split()) holes = [False]*(n+1) tmp = list(map(int,input().split())) for i in tmp: holes[i] = True if holes[1] == True: return 1 else: while k != 0: k = k-1 ...
output
1
77,243
19
154,487
Provide tags and a correct Python 3 solution for this coding contest problem. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is on the table at the position x = i. The proble...
instruction
0
77,244
19
154,488
Tags: implementation Correct Solution: ``` def inp(n): if n == 1: return map(int, stdin.readline().split()) elif n == 2: return map(float, stdin.readline().split()) else: return map(str, stdin.readline().split()) def arr_inp(): return [int(x) for x in stdin.readline().split()] ...
output
1
77,244
19
154,489
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,245
19
154,490
Yes
output
1
77,245
19
154,491
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,246
19
154,492
Yes
output
1
77,246
19
154,493
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,247
19
154,494
Yes
output
1
77,247
19
154,495
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,248
19
154,496
Yes
output
1
77,248
19
154,497
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,249
19
154,498
No
output
1
77,249
19
154,499
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,250
19
154,500
No
output
1
77,250
19
154,501
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,251
19
154,502
No
output
1
77,251
19
154,503
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Zane the wizard is going to perform a magic show shuffling the cups. There are n cups, numbered from 1 to n, placed along the x-axis on a table that has m holes on it. More precisely, cup i is ...
instruction
0
77,252
19
154,504
No
output
1
77,252
19
154,505
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,421
19
154,842
"Correct Solution: ``` import sys sys.setrecursionlimit(10000000) from math import ceil def grundy(a, k): if a < k: return 0 d, m = divmod(a, k) if m == 0: return d d1 = d + 1 if d > k: return grundy(a - d1, k) e = ceil(m / d1) * d1 return grundy(a - e, k) n = in...
output
1
77,421
19
154,843
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,422
19
154,844
"Correct Solution: ``` def main(): import sys input = sys.stdin.buffer.readline N = int(input()) win = 0 for _ in range(N): a, k = map(int, input().split()) while True: if a < k: g = 0 break elif a % k == 0: g =...
output
1
77,422
19
154,845
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,423
19
154,846
"Correct Solution: ``` def main(): n = int(input()) res = 0 for (a, k) in [map(int, input().split()) for _ in range(n)]: while a > k and a % k != 0: m = a // k x = (a - k * m - 1) // (m + 1) a -= max(1, x) * (m + 1) res ^= a // k print('Takahashi' if r...
output
1
77,423
19
154,847
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,424
19
154,848
"Correct Solution: ``` from collections import defaultdict, deque, Counter from heapq import heappush, heappop, heapify import math import bisect import random from itertools import permutations, accumulate, combinations, product import sys import string from bisect import bisect_left, bisect_right from math import fac...
output
1
77,424
19
154,849
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,425
19
154,850
"Correct Solution: ``` import sys input = sys.stdin.readline N = int(input()) AK = [list(map(int, input().split())) for _ in range(N)] # N = 40 # AK = [(i+1, 4) for i in range(N)] def grundy(A, K): if K == 1: return A X = (A+K-1)//K num = X*K - A while X*K-num > K*K: #print(X, num) ...
output
1
77,425
19
154,851
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,426
19
154,852
"Correct Solution: ``` from collections import defaultdict, deque, Counter from heapq import heappush, heappop, heapify import math import bisect import random from itertools import permutations, accumulate, combinations, product import sys import string from bisect import bisect_left, bisect_right from math import fac...
output
1
77,426
19
154,853
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,427
19
154,854
"Correct Solution: ``` import sys sys.setrecursionlimit(10 ** 8) n = int(input()) info = [list(map(int, input().split())) for i in range(n)] # 愚直解 def mex(array): if not array: return 0 set_ = set(array) for i in range(10000): if i not in set_: return i """ res = 0 for a, k i...
output
1
77,427
19
154,855
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the foll...
instruction
0
77,428
19
154,856
"Correct Solution: ``` import sys sys.setrecursionlimit(10**6) def grun(A, K): if A < K: return 0 a, b = divmod(A, K) if b == 0: return a a += 1 r = A % a return grun((((a-1)*K-r)//a)*a+r, K) def solve(): N = int(input()) X = 0 for _ in range(N): A, K = map(in...
output
1
77,428
19
154,857
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i. Starting from Takahashi, Tak...
instruction
0
77,429
19
154,858
Yes
output
1
77,429
19
154,859