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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer n. Check if n has an odd divisor, greater than one (does there exist such a number x (x > 1) that n is divisible by x and x is odd). For example, if n=6, then there is ...
instruction
0
86,869
22
173,738
No
output
1
86,869
22
173,739
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer n. Check if n has an odd divisor, greater than one (does there exist such a number x (x > 1) that n is divisible by x and x is odd). For example, if n=6, then there is ...
instruction
0
86,870
22
173,740
No
output
1
86,870
22
173,741
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,557
22
175,114
Tags: constructive algorithms, math Correct Solution: ``` from math import gcd n = int(input()) if n==3: print(1,1,3) exit() ans = [] p = 0 avail = [i+1 for i in range(n)] vis = [False for i in range(n)] while avail!=[]: # print(avail) cnt = 0 for i in range(0,len(avail),2): p = gcd(p,avail[...
output
1
87,557
22
175,115
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,558
22
175,116
Tags: constructive algorithms, math Correct Solution: ``` n = int(input()) visit = [0 for i in range(n+1)] res = [] c = 0 s,t=0,0 def do(i): global c,s,t for j in range(i,n+1,2*i): res.append(i) c += 1 if c >= (n-1) and n>2: if s == 0: s = j else: t = j return res curr = 0 i = 1 while(i<=n): # p...
output
1
87,558
22
175,117
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,559
22
175,118
Tags: constructive algorithms, math Correct Solution: ``` n = int(input()) if n == 1: print("1") elif n == 2: print("1 2") else: base = 1 gap = 2 cur = base next = 1 ans = '' for i in range(n - 1): ans += str(base) + ' ' next = cur cur += gap if cur > n: base *= 2 gap *= 2 cur = base next = m...
output
1
87,559
22
175,119
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,560
22
175,120
Tags: constructive algorithms, math Correct Solution: ``` #Complexity - O(logn) import math n = int(input()) arr = [] curr = 1 while n > 0: if n == 1: arr.append(curr) break elif n == 2: arr.append(curr) arr.append(curr*2) break elif n == 3: arr.append(curr) arr.append(curr*1) a...
output
1
87,560
22
175,121
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,561
22
175,122
Tags: constructive algorithms, math Correct Solution: ``` import os import sys from io import BytesIO, IOBase import math # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in f...
output
1
87,561
22
175,123
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,562
22
175,124
Tags: constructive algorithms, math Correct Solution: ``` n=int(input()) def cal(n,t): if n==1: print(t,end=' ') elif n==2: print(t,t<<1,end=' ') elif n==3: print(t,t,t*3, end=' ') else: tmp=n-(n>>1) for i in range(tmp): print(t,end=' ') cal(n>...
output
1
87,562
22
175,125
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,563
22
175,126
Tags: constructive algorithms, math Correct Solution: ``` #copying............................................. n,t=int(input()),1 while n>0: if n!=3: k=n//2+n%2 print((str(t)+' ')*k,end='') n-=k t*=2 else: print(t,t,t*3) n=0 ```
output
1
87,563
22
175,127
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) (GCD) of all the...
instruction
0
87,564
22
175,128
Tags: constructive algorithms, math Correct Solution: ``` from sys import stdin,stdout,exit,setrecursionlimit def sin(): return stdin.readline().rstrip() def listInput(): return list(map(int,sin().split())) def printBS(li): if not li: return for i in range(len(li)-1): stdout.write("%d "%(li[i])) stdout.write("%...
output
1
87,564
22
175,129
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,565
22
175,130
Yes
output
1
87,565
22
175,131
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,566
22
175,132
Yes
output
1
87,566
22
175,133
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,567
22
175,134
Yes
output
1
87,567
22
175,135
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,568
22
175,136
Yes
output
1
87,568
22
175,137
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,569
22
175,138
No
output
1
87,569
22
175,139
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,570
22
175,140
No
output
1
87,570
22
175,141
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,571
22
175,142
No
output
1
87,571
22
175,143
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call the following process a transformation of a sequence of length n. If the sequence is empty, the process ends. Otherwise, append the [greatest common divisor](https://en.wikipedia.org...
instruction
0
87,572
22
175,144
No
output
1
87,572
22
175,145
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,527
22
177,054
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` t = int(input()) for i in range(t): x = int(input()) print("1", x - 1) ```
output
1
88,527
22
177,055
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,528
22
177,056
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` t=int(input()) for testcase in range(t): sum=int(input()) print(1,sum-1) ```
output
1
88,528
22
177,057
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,529
22
177,058
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` t = int(input()) while t: x = int(input()) print('1 ', x - 1) t -= 1 ```
output
1
88,529
22
177,059
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,530
22
177,060
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` n=int(input()) for i in range(n): n1=int(input()) print(1,n1-1) ```
output
1
88,530
22
177,061
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,531
22
177,062
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` for i in range(int(input())): n=int(input()) print(1,n-1,end=' ') ```
output
1
88,531
22
177,063
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,532
22
177,064
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` t = int(input()) count = 0 ans = [] while count < t : x = int(input()) ans.append(x) count +=1 for y in ans: print ("1" , y-1) ...
output
1
88,532
22
177,065
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,533
22
177,066
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` cases=int(input()) for case in range(cases): number=int(input()) for i in range(1,number//2+1): if (number-i)%i==0: print(i,number-i) break ```
output
1
88,533
22
177,067
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly, LCM(a,b) is the smallest integer such that bo...
instruction
0
88,534
22
177,068
Tags: constructive algorithms, greedy, number theory Correct Solution: ``` t = int(input()) for tc in range(t): x = int(input()) a = x-1 b = 1 print(a, b) ```
output
1
88,534
22
177,069
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,535
22
177,070
Yes
output
1
88,535
22
177,071
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,536
22
177,072
Yes
output
1
88,536
22
177,073
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,537
22
177,074
Yes
output
1
88,537
22
177,075
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,538
22
177,076
Yes
output
1
88,538
22
177,077
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,539
22
177,078
No
output
1
88,539
22
177,079
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,540
22
177,080
No
output
1
88,540
22
177,081
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,541
22
177,082
No
output
1
88,541
22
177,083
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive integer x. Find any such 2 positive integers a and b such that GCD(a,b)+LCM(a,b)=x. As a reminder, GCD(a,b) is the greatest integer that divides both a and b. Similarly...
instruction
0
88,542
22
177,084
No
output
1
88,542
22
177,085
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,801
22
177,602
Tags: brute force, implementation, math, number theory Correct Solution: ``` def gcd(a, b): if(a == 0 or b == 0): return a + b else: return gcd(b, a % b); l, r = map(int, input().split()) r = r + 1 for a in range(l, r): for b in range(a + 1, r): for c in range(b + 1, r): if(gcd(a, b) ==...
output
1
88,801
22
177,603
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,802
22
177,604
Tags: brute force, implementation, math, number theory Correct Solution: ``` import sys le, rg = map(int, input().split()) rg += 1 def gcd(a, b): while b: a, b = b, a % b return a for a in range(le, rg): for b in range(a + 1, rg): gab = gcd(a, b) if gab != 1: continue ...
output
1
88,802
22
177,605
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,803
22
177,606
Tags: brute force, implementation, math, number theory Correct Solution: ``` l, r = map(int, input().split()) if r - l + 1 < 3 or (r - l + 1 == 3 and l % 2 == 1): print(-1) else: base = l % 2 + l ans = [base, base+1, base+2] print(*ans, sep=' ') ```
output
1
88,803
22
177,607
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,804
22
177,608
Tags: brute force, implementation, math, number theory Correct Solution: ``` inp = input().split(' ') a = int(inp[0]) b = int(inp[1]) if (b-a)<2: print(-1) elif (b-a) == 2 and b%2 == 1: print(-1) else: if a%2 == 1: a = a + 1 print(a,a+1,a+2) ```
output
1
88,804
22
177,609
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,805
22
177,610
Tags: brute force, implementation, math, number theory Correct Solution: ``` # t=int(input()) t=1 # see u codeforces on 11-07-2020..bye bye for _ in range(t): # n=int(input()) n,m=map(int,input().split()) # l=list(map(int,input().split())) if(n&1): n+=1 if(n+2>m): print(-1) else: print(n,n+1,n+2) ```
output
1
88,805
22
177,611
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,806
22
177,612
Tags: brute force, implementation, math, number theory Correct Solution: ``` import sys,random def gcd(x,y): if y==0: return x else: return gcd(y,x%y) def pollard(n): i = 1 x = random.randint(0,n-1) y = x k = 2 while True: i = i+1 x = (x*x - 1)%n d = ...
output
1
88,806
22
177,613
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,807
22
177,614
Tags: brute force, implementation, math, number theory Correct Solution: ``` l, r = map(int, input().split()) if l % 2 != 0: l += 1 if l + 2 > r: print(-1) else: print(l, l+1, l+2) ```
output
1
88,807
22
177,615
Provide tags and a correct Python 3 solution for this coding contest problem. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently suppo...
instruction
0
88,808
22
177,616
Tags: brute force, implementation, math, number theory Correct Solution: ``` if __name__ == '__main__': l, r = [int(i) for i in input().split()] if r - l < 2: print(-1) elif l % 2 == 0: print(l, l + 1, l + 2) elif r - l > 2: print(l + 1, l + 2, l + 3) else: print(-1) ```
output
1
88,808
22
177,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,809
22
177,618
Yes
output
1
88,809
22
177,619
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,810
22
177,620
Yes
output
1
88,810
22
177,621
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,811
22
177,622
Yes
output
1
88,811
22
177,623
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,812
22
177,624
Yes
output
1
88,812
22
177,625
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,813
22
177,626
No
output
1
88,813
22
177,627
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,814
22
177,628
No
output
1
88,814
22
177,629
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,815
22
177,630
No
output
1
88,815
22
177,631
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up w...
instruction
0
88,816
22
177,632
No
output
1
88,816
22
177,633