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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Positive integer x is called divisor of positive integer y, if y is divisible by x without remainder. For example, 1 is a divisor of 7 and 3 is not divisor of 8. We gave you an integer d and as...
instruction
0
45,619
22
91,238
No
output
1
45,619
22
91,239
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,844
22
91,688
Tags: brute force, constructive algorithms, math Correct Solution: ``` from math import * n= int(input()) if n%2==1: print((n-1)//2,(n-1)//2+1 ) else: r= n//2 for i in reversed(range(1,r)): if gcd(i,n-i)==1: print(i,n-i); exit(0) ```
output
1
45,844
22
91,689
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,845
22
91,690
Tags: brute force, constructive algorithms, math Correct Solution: ``` a=int(input()) thesum=0 if a%2==0: firstnumber=int(a/2) secondnumber=int(a/2) elif a%2==1: firstnumber=int((a-1)/2) secondnumber=int((a+1)/2) killnumber=0 primenumber=2 rocketnumber=0 while rocketnumber==0: while killnumber==0 ...
output
1
45,845
22
91,691
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,846
22
91,692
Tags: brute force, constructive algorithms, math Correct Solution: ``` from fractions import gcd import math n = int(input()) a = 0 b = 0 x = int(n/2) + 1 for i in range(1,x): if gcd(i, n-i) == 1: a = i b = n - i # print(a,b) print(a,b) ```
output
1
45,846
22
91,693
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,847
22
91,694
Tags: brute force, constructive algorithms, math Correct Solution: ``` import math n=int(input()) if n%2==1: a,b=n//2,n//2+1 else: a,b=n//2-1, n//2+1 while math.gcd(a,b)!=1: a-=1 b+=1 print(a,b) ```
output
1
45,847
22
91,695
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,848
22
91,696
Tags: brute force, constructive algorithms, math Correct Solution: ``` from math import gcd as bltin_gcd def coprime(a, b): return bltin_gcd(a, b) == 1 def II(): return int(SI()) # def MI(): return map(int, SI().split()) # def LI(): return list(MI()) def SI(): return input() N = II() pairs = [] for a ...
output
1
45,848
22
91,697
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,849
22
91,698
Tags: brute force, constructive algorithms, math Correct Solution: ``` #!/usr/bin/env python3 # -*- coding: utf-8 -*- def irr(a, b): for k in range(1, a + 1): if a % k == 0 and b % k == 0 and k != 1: return False return True def gener(n): l = [] for i in range(1, n // 2): ...
output
1
45,849
22
91,699
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,850
22
91,700
Tags: brute force, constructive algorithms, math Correct Solution: ``` def gcd(a, b): if b < a: return gcd(b, a) if b%a==0: return a return gcd(b%a, a) total = int(input()) num = total // 2 den = total - num while True: if gcd(num, den)==1: print(num, den) break num-=1 den+=1 ```
output
1
45,850
22
91,701
Provide tags and a correct Python 3 solution for this coding contest problem. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible i...
instruction
0
45,851
22
91,702
Tags: brute force, constructive algorithms, math Correct Solution: ``` n = int(input()) from fractions import gcd for a in reversed(range(1,n//2+1)): b = n-a if gcd(a,b) == 1: print(a,b) break ```
output
1
45,851
22
91,703
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,852
22
91,704
Yes
output
1
45,852
22
91,705
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,853
22
91,706
Yes
output
1
45,853
22
91,707
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,854
22
91,708
Yes
output
1
45,854
22
91,709
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,855
22
91,710
Yes
output
1
45,855
22
91,711
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,856
22
91,712
No
output
1
45,856
22
91,713
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,857
22
91,714
No
output
1
45,857
22
91,715
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,858
22
91,716
No
output
1
45,858
22
91,717
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b...
instruction
0
45,859
22
91,718
No
output
1
45,859
22
91,719
Provide a correct Python 3 solution for this coding contest problem. Fibonacci number f(i) appear in a variety of puzzles in nature and math, including packing problems, family trees or Pythagorean triangles. They obey the rule f(i) = f(i - 1) + f(i - 2), where we set f(0) = 1 = f(-1). Let V and d be two certain posi...
instruction
0
46,118
22
92,236
"Correct Solution: ``` # AOJ 1016: Fibonacci Sets # Python3 2018.7.4 bal4u f = [0]*1001 f[0], f[1] = 2, 3 for i in range(2, 1001): f[i] = (f[i-1]+f[i-2])%1001 while True: try: V, d = map(int, input().split()) except: break ans, a = 1, sorted(f[:V]) for i in range(1, V): if a[i]-a[i-1] >= d: ans += 1 print(ans) ...
output
1
46,118
22
92,237
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,414
22
92,828
Tags: math Correct Solution: ``` import sys content = sys.stdin.read().strip().splitlines() content = content[1:] def f(n): divisor = 0 for i in range(2, int(n ** 0.5) + 1): if n % i == 0: divisor = i break if divisor == 0: divisor = n return divisor for c in co...
output
1
46,414
22
92,829
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,415
22
92,830
Tags: math Correct Solution: ``` for _ in range(int(input())): n, k = map(int, input().split()) if n % 2 == 0: n += 2 * k else: if k == 1: n = 2 * n else: backUp = 0 for i in range(3, n + 1, 2): if n % i == 0: ba...
output
1
46,415
22
92,831
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,416
22
92,832
Tags: math Correct Solution: ``` for _ in range(int(input())): n,k = map(int,input().split()) if(n%2==0): n=2*(k)+n else: for i in range(3,n+1,2): if(n%i)==0: # print(i) n=n+i break n=2*(k-1)+n print(n) ...
output
1
46,416
22
92,833
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,417
22
92,834
Tags: math Correct Solution: ``` def f(n): i = 2 while i * i <= n: if n % i == 0: return i i += 1 return n def solve(n, k): return n + f(n) + 2 * (k - 1) [print(solve(*map(int, input().split()))) for t in range(int(input()))] ```
output
1
46,417
22
92,835
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,418
22
92,836
Tags: math Correct Solution: ``` def f(x): if x % 2 == 0: return 2 i=3 val=x # if while loop doesnt change the value, then the no is prime, so the output should be the no. itself while(i*i<=x): if(x%i==0): val=i break else: i+=2 return val ...
output
1
46,418
22
92,837
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,419
22
92,838
Tags: math Correct Solution: ``` def func(N): if N==1: return 1 elif N%2==0: return 2 else: for i in range(3,int(N/3)+1): if N%i==0: return i return N T=int(input()) for t in range(T): [N,K]=list(map(int,input().strip().split())) N+=func(N...
output
1
46,419
22
92,839
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,420
22
92,840
Tags: math Correct Solution: ``` import sys from math import log,sqrt,factorial def ii(): return int(input()) def si(): return input() def mi(): return map(int,input().strip().split(" ")) def msi(): return map(str,input().strip().split(" ")) def li(): return list(mi()) #def read(): t=ii() while(t): t-=1 n,...
output
1
46,420
22
92,841
Provide tags and a correct Python 3 solution for this coding contest problem. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b. For n ≥ 2, we will denote as f(n) the sm...
instruction
0
46,421
22
92,842
Tags: math Correct Solution: ``` def f(a): b = 2; while a % b > 0: b += 1 return b for _ in range(int(input())): n, k = [int(x) for x in input().split()] if not (n % 2): print(n + 2 * k) continue x = f(n) print(n + x + 2 * (k-1)) ```
output
1
46,421
22
92,843
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,422
22
92,844
Yes
output
1
46,422
22
92,845
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,423
22
92,846
Yes
output
1
46,423
22
92,847
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,424
22
92,848
Yes
output
1
46,424
22
92,849
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,425
22
92,850
Yes
output
1
46,425
22
92,851
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,426
22
92,852
No
output
1
46,426
22
92,853
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,427
22
92,854
No
output
1
46,427
22
92,855
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,428
22
92,856
No
output
1
46,428
22
92,857
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,429
22
92,858
No
output
1
46,429
22
92,859
Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,430
22
92,860
No
output
1
46,430
22
92,861
Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response. Orac is studying number theory, and he is interested in the properties of divisors. For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅...
instruction
0
46,431
22
92,862
No
output
1
46,431
22
92,863
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,496
22
92,992
Tags: binary search, brute force, math, number theory Correct Solution: ``` from bisect import * from collections import * from math import gcd,ceil,sqrt,floor,inf from heapq import * from itertools import * from operator import add,mul,sub,xor,truediv,floordiv from functools import * #-------------------------------...
output
1
46,496
22
92,993
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,497
22
92,994
Tags: binary search, brute force, math, number theory Correct Solution: ``` # for a in range(1,50): # for b in range(1,50): # left=(a//b) # right=a%b # if left==right: # print(a,b) al=[] for _ in range(int(input())): x,y=map(int, input().split()) ans=0 for r in range...
output
1
46,497
22
92,995
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,498
22
92,996
Tags: binary search, brute force, math, number theory Correct Solution: ``` ''' Aaditya Upadhyay ud$$$**$$$$$$bc. u@**" 4$$$$$$Nu J ""#$$$$$r @ $$$b .F ...
output
1
46,498
22
92,997
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,499
22
92,998
Tags: binary search, brute force, math, number theory Correct Solution: ``` def testcase(): [X,Y]=[int(c) for c in input().split()] res = 0 b = 1 while b**2-1 <= X and b <= Y: res += b-1 #b-1 valid a b += 1 c = 1 #number of valid a while c < b: hi = (X//c)-1 lo =...
output
1
46,499
22
92,999
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,500
22
93,000
Tags: binary search, brute force, math, number theory Correct Solution: ``` t=int(input()) for _ in range(t): a,b=map(int,input().split()) ans=0 c=1 while c*c<=a: x = (a-c)//c if x>b: x=b ans+=max(x-c,0) c+=1 print(ans) ```
output
1
46,500
22
93,001
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,501
22
93,002
Tags: binary search, brute force, math, number theory Correct Solution: ``` import collections import string import math import copy import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.b...
output
1
46,501
22
93,003
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,502
22
93,004
Tags: binary search, brute force, math, number theory Correct Solution: ``` t = int(input()) for i in range(t): l1 = input().split(' ') x, y = int(l1[0]), int(l1[1]) s = 0 for j in range(1, y): k = (x-j) // j if k <= j : break s += min(k, y) - j # print(j, s)...
output
1
46,502
22
93,005
Provide tags and a correct Python 3 solution for this coding contest problem. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two integers x and y. Find the number of special pa...
instruction
0
46,503
22
93,006
Tags: binary search, brute force, math, number theory Correct Solution: ``` def main(): t=int(input()) allAns=[] for _ in range(t): x,y=readIntArr() ans=0 nK=1 while min((x//nK-1),y)>=nK: ans+=min((x//nK-1),y)-nK nK+=1 allAns.app...
output
1
46,503
22
93,007
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,504
22
93,008
Yes
output
1
46,504
22
93,009
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,505
22
93,010
Yes
output
1
46,505
22
93,011
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,506
22
93,012
Yes
output
1
46,506
22
93,013
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,507
22
93,014
Yes
output
1
46,507
22
93,015
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,508
22
93,016
No
output
1
46,508
22
93,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder. You are given two ...
instruction
0
46,509
22
93,018
No
output
1
46,509
22
93,019