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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,622
22
139,244
Yes
output
1
69,622
22
139,245
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,623
22
139,246
Yes
output
1
69,623
22
139,247
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,624
22
139,248
Yes
output
1
69,624
22
139,249
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,625
22
139,250
No
output
1
69,625
22
139,251
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,626
22
139,252
No
output
1
69,626
22
139,253
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,627
22
139,254
No
output
1
69,627
22
139,255
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x. W...
instruction
0
69,628
22
139,256
No
output
1
69,628
22
139,257
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,792
22
139,584
"Correct Solution: ``` # http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=NTL_1_A&lang=ja def prime_factors(n): # 戻り値はiterable type i = 2 while i * i <= n: if n % i: i += 1 else: n //= i yield i if n > 1: yield n N = int(input()) P...
output
1
69,792
22
139,585
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,793
22
139,586
"Correct Solution: ``` n=int(input()) A=[] B=n while n%2==0: n//=2 A.append(2) while n%3==0: n//=3 A.append(3) while n%5==0: n//=5 A.append(5) while n%7==0: n//=7 A.append(7) if n>=10000000: A.append(n) else: for j in range(3,n+1,2): while n%j==0: n//=j ...
output
1
69,793
22
139,587
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,794
22
139,588
"Correct Solution: ``` def factorization(n): L=[] temp=n print(n,end="") print(":",end="") for i in range(2,int(n**(1/2)//1)+1): if temp%i==0: c=0 while temp%i==0: c+=1 temp//=i L.append([i,c]) for j in range(c):...
output
1
69,794
22
139,589
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,795
22
139,590
"Correct Solution: ``` from math import sqrt n = int(input()) def prime_factors(N): a = [] while N % 2 == 0: a.append(2) N //= 2 f = 3 while f * f <= N: if N % f == 0: a.append(f) N //= f else: f += 2 if N != 1: a.append(N...
output
1
69,795
22
139,591
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,796
22
139,592
"Correct Solution: ``` n=int(input()) def prime_factorize(n): a = [] while n % 2 == 0: a.append(2) n //= 2 f = 3 while f * f <= n: if n % f == 0: a.append(f) n //= f else: f += 2 if n != 1: a.append(n) return a b=prime_f...
output
1
69,796
22
139,593
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,797
22
139,594
"Correct Solution: ``` def prime_factor(n): ass = [] for i in range(2,int(n**0.5)+1): while n % i==0: ass.append(i) n = n//i if n != 1: ass.append(n) return ass a = int(input()) print(str(a)+': ',end='') print(*prime_factor(a)) ```
output
1
69,797
22
139,595
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,798
22
139,596
"Correct Solution: ``` n=int(input()) n1=n l=[] def isprime(n): if n==2: return True elif n==1: return False else: for i in range(2,int(n**0.5)+1): if n%i==0: return False return True for i in range(2,int(n**0.5)+1): while n1%i==0: l.append(i) n1=n1//i if isprime(n1): ...
output
1
69,798
22
139,597
Provide a correct Python 3 solution for this coding contest problem. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prim...
instruction
0
69,799
22
139,598
"Correct Solution: ``` n = int(input()) m = int(n**0.5)+2 is_prime = [1]*m is_prime[0] = is_prime[1] = 0 for p in range(2,m): for q in range(2*p,m,p): is_prime[q] = 0 primes = [p for p, c in enumerate(is_prime) if c] print(str(n)+': ', end='') ans = [] for p in primes: while n % p == 0: ans.app...
output
1
69,799
22
139,599
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,800
22
139,600
Yes
output
1
69,800
22
139,601
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,801
22
139,602
Yes
output
1
69,801
22
139,603
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,802
22
139,604
Yes
output
1
69,802
22
139,605
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,803
22
139,606
Yes
output
1
69,803
22
139,607
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,804
22
139,608
No
output
1
69,804
22
139,609
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,805
22
139,610
No
output
1
69,805
22
139,611
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,806
22
139,612
No
output
1
69,806
22
139,613
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Factorize a given integer n. Constraints * 2 ≤ n ≤ 109 Input n An integer n is given in a line. Output Print the given integer n and :. Then, print prime factors in ascending order. If ...
instruction
0
69,807
22
139,614
No
output
1
69,807
22
139,615
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the s...
instruction
0
70,139
22
140,278
Yes
output
1
70,139
22
140,279
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,475
22
140,950
Tags: implementation, math Correct Solution: ``` print('\n'.join(('F','Inf')[pow(b,64,q)*p%q>0]+'inite'for p,q,b in(map(int,input().split())for _ in[0]*int(input())))) ```
output
1
70,475
22
140,951
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,476
22
140,952
Tags: implementation, math Correct Solution: ``` import sys def main(): n = int(input()) ans = [] for i in range(n): p, q, b = map(int, input().split(" ")) t = pow(b, 111, q) if p * t % q == 0: ans.append("Finite") else: ans.append("Infinite") pr...
output
1
70,476
22
140,953
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,477
22
140,954
Tags: implementation, math Correct Solution: ``` # python3 import sys from fractions import gcd def is_finite(p, q, b): return not p * pow(b, 64, q) % q input() print("\n".join("Finite" if is_finite(*map(int, line.split())) else "Infinite" for line in sys.stdin.readlines())) ```
output
1
70,477
22
140,955
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,478
22
140,956
Tags: implementation, math Correct Solution: ``` import sys input() out = [] for line in sys.stdin: p,q,b=[int(x) for x in line.split()] out.append(['Finite','Infinite'][bool(p*pow(b,60,q)%q)]) print('\n'.join(out)) ```
output
1
70,478
22
140,957
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,479
22
140,958
Tags: implementation, math Correct Solution: ``` import sys import math ini = lambda: int(sys.stdin.readline()) inl = lambda: [int(x) for x in sys.stdin.readline().split()] def solve(): p, q, b = inl() if p == 0: return True g = math.gcd(p, q) p //= g q //= g if q == 1: return...
output
1
70,479
22
140,959
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,480
22
140,960
Tags: implementation, math Correct Solution: ``` input() print('\n'.join(map(lambda x: (lambda p, q, b: 'Infinite' if p * pow(b, 60, q) % q else 'Finite')(*x), map(lambda l:map(int, l.split()), __import__('sys').stdin.readlines())))) ```
output
1
70,480
22
140,961
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,481
22
140,962
Tags: implementation, math Correct Solution: ``` n=int(input()) s='' for i in range(n): p,q,b=map(int,input().split()) for i in range(6): b=(b*b)%q if((p*b)%q): s+='Infinite\n' else: s+='Finite\n' print(s) ```
output
1
70,481
22
140,963
Provide tags and a correct Python 3 solution for this coding contest problem. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notation with base b is finite if it contains finite n...
instruction
0
70,482
22
140,964
Tags: implementation, math Correct Solution: ``` from sys import stdin, stdout n=int(stdin.readline()) s='' for i in range(n): p,q,b=map(int,input().split()) for i in range(6): b=(b*b)%q if((p*b)%q): s+='Infinite\n' else: s+='Finite\n' print(s) ```
output
1
70,482
22
140,965
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,483
22
140,966
Yes
output
1
70,483
22
140,967
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,484
22
140,968
Yes
output
1
70,484
22
140,969
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,486
22
140,972
Yes
output
1
70,486
22
140,973
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,487
22
140,974
No
output
1
70,487
22
140,975
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,488
22
140,976
No
output
1
70,488
22
140,977
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b is a finite fraction. A fraction in notatio...
instruction
0
70,490
22
140,980
No
output
1
70,490
22
140,981
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Janusz is a businessman. He owns a company "Januszex", which produces games for teenagers. Last hit of Januszex was a cool one-person game "Make it one". The player is given a sequence of n inte...
instruction
0
70,741
22
141,482
No
output
1
70,741
22
141,483
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Janusz is a businessman. He owns a company "Januszex", which produces games for teenagers. Last hit of Januszex was a cool one-person game "Make it one". The player is given a sequence of n inte...
instruction
0
70,742
22
141,484
No
output
1
70,742
22
141,485
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Janusz is a businessman. He owns a company "Januszex", which produces games for teenagers. Last hit of Januszex was a cool one-person game "Make it one". The player is given a sequence of n inte...
instruction
0
70,743
22
141,486
No
output
1
70,743
22
141,487
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Janusz is a businessman. He owns a company "Januszex", which produces games for teenagers. Last hit of Januszex was a cool one-person game "Make it one". The player is given a sequence of n inte...
instruction
0
70,744
22
141,488
No
output
1
70,744
22
141,489
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,777
22
141,554
Tags: brute force, greedy, math, number theory Correct Solution: ``` def factors(number): factors=[] for i in range(1,number+1): if number%i==0: factors.append(i) return factors n=int(input()) fac=input().split() fac=list(map(int,fac)) number=max(fac) for x in factors(number): fac...
output
1
70,777
22
141,555
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,778
22
141,556
Tags: brute force, greedy, math, number theory Correct Solution: ``` n = int(input()) d = list(map(int, input().split())) x = max(d) if d.count(x) == 2: print(x, x) else: setd = set(d) notx = [] y = [] for i in setd: if x % i != 0: notx.append(i) if len(notx) != 0: pr...
output
1
70,778
22
141,557
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,779
22
141,558
Tags: brute force, greedy, math, number theory Correct Solution: ``` import math n = eval(input()) array = list(map(int, input().split())) array.sort() x = array[-1] arr = [] max1 = -1 for i in array: if(x%i!=0 or (x%i==0 and array.count(i)==2)): max1 = max(max1, i) y = max1 print(x, y) ```
output
1
70,779
22
141,559
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,780
22
141,560
Tags: brute force, greedy, math, number theory Correct Solution: ``` n=int(input()) d=input().split() a=[0 for j in range(10**4+1)] for i in range(n): d[i]=int(d[i]) a[d[i]]+=1 d.sort(reverse=True) x=d[0] for j in range(1,x+1): if(x%j==0): a[j]-=1 for l in range(10**4+1): if(a[l]==1): y=...
output
1
70,780
22
141,561
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,781
22
141,562
Tags: brute force, greedy, math, number theory Correct Solution: ``` n = int(input()) a = [int(j) for j in input().split()] x = max(a) y=1 for i in range(1,x+1): if x%i == 0: a.remove(i) y=max(a) print(x,y) # print(a) ```
output
1
70,781
22
141,563
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,782
22
141,564
Tags: brute force, greedy, math, number theory Correct Solution: ``` n = int(input()) lst = [int(j) for j in input().split(' ') if j!='' and j!=' '] lst.sort() num1 = lst[-1] print(num1,end=' ') i = 1 while i<=num1: if num1%i==0: lst.remove(i) i+=1 print(lst[-1]) ```
output
1
70,782
22
141,565
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,783
22
141,566
Tags: brute force, greedy, math, number theory Correct Solution: ``` def ls(l,n): # l = [l[i] for i in range(0,n)] desc = sorted(l,reverse=True) n1 = desc[0] l1 = [] l2 = [] for i in range(1,len(desc)): if (n1 % desc[i])or desc.count(desc[i])>1: l1.append(desc[i]) el...
output
1
70,783
22
141,567
Provide tags and a correct Python 3 solution for this coding contest problem. Recently you have received two positive integer numbers x and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both number...
instruction
0
70,784
22
141,568
Tags: brute force, greedy, math, number theory Correct Solution: ``` N = int(input()) A = list(map(int, input().split())) X = max(A) div = set() for i in range(1, int(X ** (1/2)) + 2): if X % i == 0: div.add(i) div.add(X // i) f = [] for a in A: if a in div: div.remove(a) else: ...
output
1
70,784
22
141,569