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Provide a correct Python 3 solution for this coding contest problem. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. Input Input is given from Standard Input in the following format: N Output Print the answer in a line. Examples Input 11 Output 10 Input 20200920 Output 1100144
instruction
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"Correct Solution: ``` def inv_gcd(a, b): a = (a + b) % b if a == 0: return (b, 0) s, t = b, a m0, m1 = 0, 1 while t: u = s // t s -= t * u m0 -= m1 * u tmp = s s = t t = tmp tmp = m0 m0 = m1 m1 = tmp if m0 < 0: m0 += b // s return (s, m0) def crt(r, m): n = len(r) r0, m0 = 0, 1 for i in range(n): r1, m1 = (r[i] + m[i]) % m[i], m[i] if m0 < m1: m0, m1 = m1, m0 r0, r1 = r1, r0 if m0 % m1 == 0: if r0 % m1 != r1: return (0, 0) continue g, im = inv_gcd(m0, m1) u1 = m1 // g if (r1 - r0) % g: return (0, 0) x = (r1 - r0) // g % u1 * im % u1 r0 += x * m0 m0 *= u1 if (r0 < 0): r0 += m0 return (r0, m0) def divisors(n): divisors = [] for i in range(1, int(n**0.5)+1): if n % i == 0: divisors.append(i) if i != n // i: divisors.append(n//i) divisors.sort() return divisors # print(divisors(z)) z=int(input()) ans = z-1 if z%2 else 2*z-1 for i in divisors(2*z): y=2*z//i if y == 1: continue a=[0,-1] b=[i,y] rem, mod = crt(a, b) #print(rem) #print(mod) if rem == mod == 0: continue ans = min(ans, rem) print(ans if z-1 else 1) ```
output
1
14,760
22
29,521
Provide a correct Python 3 solution for this coding contest problem. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. Input Input is given from Standard Input in the following format: N Output Print the answer in a line. Examples Input 11 Output 10 Input 20200920 Output 1100144
instruction
0
14,764
22
29,528
"Correct Solution: ``` def egcd(a, b): if a == 0: return (b, 0, 1) else: g, y, x = egcd(b % a, a) return (g, x - (b // a) * y, y) def modinv(a, m): g, x, y = egcd(a, m) if g != 1: raise Exception('modular inverse does not exist') else: return x % m N = int(input()) N *= 2 def crt(a, n, b, m, inv): out = a #inv = pow(n, -1, m) out += (b - a) * n * inv return out % (n * m) p = [] i = 2 while i * i <= N: curr = 1 while N % i == 0: N//= i curr *= i if curr != 1: p.append(curr) i += 1 if N != 1: p.append(N) poss = [0] mod = 1 for v in p: new = [] #inv = pow(mod, -1, v) inv = modinv(mod, v) for u in poss: new.append(crt(u, mod, 0, v, inv)) new.append(crt(u, mod, -1, v, inv)) poss = new mod *= v poss.sort() poss += [mod] print(poss[1]) ```
output
1
14,764
22
29,529
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. Input Input is given from Standard Input in the following format: N Output Print the answer in a line. Examples Input 11 Output 10 Input 20200920 Output 1100144 Submitted Solution: ``` from math import gcd from collections import Counter from itertools import product min2 = lambda x,y: x if x < y else y # 拡張ユークリッド互除法 # ax + by = gcd(a,b)の最小整数解を返す 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) # mを法とするaの乗法的逆元 def modinv(a, m): g, x, y = egcd(a, m) if g != 1: raise Exception('modular inverse does not exist') else: return x % m def chinese_remainder_theorem(R, M, prod): """ returns x s.t. all(x%m == r for r,m in zip(R,M)) """ s = 0 for m,r in zip(M,R): p = prod//m s += r * p * modinv(p,m) s %= prod return s # 素因数分解 def prime_factors(n): i = 2 while i * i <= n: if n % i: i += 1 else: n //= i yield i if n > 1: yield n N = int(input()) factors = Counter(prime_factors(N)) if factors[2] > 0: factors[2] += 1 N *= 2 mods = [f**p for f,p in factors.items()] res = N for R in product(*((0,m-1) for m in mods)): t = chinese_remainder_theorem(R, mods, N) if t > 0: res = min2(res, t) print(res) ```
instruction
0
14,767
22
29,534
Yes
output
1
14,767
22
29,535
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists. Constraints * 1 \leq N \leq 10^{15} * All values in input are integers. Input Input is given from Standard Input in the following format: N Output Print the answer in a line. Examples Input 11 Output 10 Input 20200920 Output 1100144 Submitted Solution: ``` from itertools import product def main(): n = int(input()) # Exception Handling if n == 1: print(1) exit() # calculate the maximum answer if n % 2 == 0: ans = 2 * n - 1 n *= 2 else: ans = n - 1 # Prime Factorization factors = [] for p in range(2, n): if p * p > n: if n > 1: factors.append(n) break if n % p == 0: cnt = 0 while n % p == 0: cnt += 1 n //= p factors.append(p ** cnt) # Full Search # k%factor==0 or (k+1)%factor==0 for tf in product([True, False], repeat=len(factors)): a, b = 1, 1 for i in range(len(factors)): if tf[i]: a *= factors[i] else: b *= factors[i] if a < b or a == 1 or b == 1: continue # Euclidean Algorithm # a*x - b*y = 1 l = [] quo = [] while a % b > 1: l.append(a) a = b quo.append(0) quo[-1], b = divmod(l[-1], b) x, y = 1, a//b flag = True while l: if flag: x += y * quo.pop() b = l.pop() else: y += x * quo.pop() a = l.pop() flag = not flag if ans > b * y: ans = b * y print(ans) main() ```
instruction
0
14,768
22
29,536
Yes
output
1
14,768
22
29,537
Provide tags and a correct Python 3 solution for this coding contest problem. Input The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space. Output Output "YES" or "NO". Examples Input 2 3 Output YES Input 3 2 Output NO Input 33 16 Output YES Input 26 5 Output NO
instruction
0
15,312
22
30,624
Tags: *special, number theory Correct Solution: ``` import sys import collections def int2base(dec, base): ans = [] while(dec > 0): ans.insert(0,dec % base) dec //= base return ans def xenodrome(num_list): most_common = collections.Counter(num_list).most_common(1) return most_common[0][1] == 1 while(True): try: num,base = map(int, input().split()) candidate = int2base(num,base) if(xenodrome(candidate)): print("YES") else: print("NO") except EOFError: break ```
output
1
15,312
22
30,625
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,374
22
30,748
Tags: brute force, number theory, sortings Correct Solution: ``` n=int(input()) a=list(map(int,input().split())) m=min(a) for i in range(n): if a[i]%m!=0: print(-1) exit() print(m) ```
output
1
15,374
22
30,749
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,375
22
30,750
Tags: brute force, number theory, sortings Correct Solution: ``` a = int(input()) array = list(map(int, input().split())) array.sort() count = 0 for i in array[1:]: if i % array[0] == 0: count += 1 continue else: break if count == len(array) - 1: print(array[0]) else: print(-1) ```
output
1
15,375
22
30,751
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,376
22
30,752
Tags: brute force, number theory, sortings Correct Solution: ``` from math import * n=int(input()) l=list(map(int,input().split())) g=l[0] for i in range(1,n): g=gcd(g,l[i]) if(g in l): print(g) else: print(-1) ```
output
1
15,376
22
30,753
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,377
22
30,754
Tags: brute force, number theory, sortings Correct Solution: ``` f,n,l=0,int(input()),sorted(map(int,input().split())) for x in range(n): if l[x]%l[0]!=0:f=1;break print([l[0],-1][f==1]) ```
output
1
15,377
22
30,755
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,378
22
30,756
Tags: brute force, number theory, sortings Correct Solution: ``` n, t = int(input()), list(map(int, input().split())) k = min(t) print(-1 if any(i % k for i in t) else k) ```
output
1
15,378
22
30,757
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,379
22
30,758
Tags: brute force, number theory, sortings Correct Solution: ``` from math import gcd n = int(input()) arr = [int(x) for x in input().split()];g = arr[0] for i in arr: g = gcd(g,i) if g in arr: print(g) else: print(-1) ```
output
1
15,379
22
30,759
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,380
22
30,760
Tags: brute force, number theory, sortings Correct Solution: ``` def gcd(a, b): factor = a while b%factor != 0: temp = factor factor = b%factor b = temp return(factor) def main(): n = int(input()) arr = list(map(int, input().split(" "))) if n == 1: print(arr[0]) return factor = gcd(arr[0], arr[1]) found = 1 if factor in (arr[0], arr[1]) else 0 # print(factor, found) count = 2 while count < n: if factor != 1: cd = gcd(factor, arr[count]) if cd != factor and cd != arr[count]: found = 0 else: found = 1 factor = cd else: if arr[count] == 1: found = 1 break count += 1 # print(factor, found) if found: print(factor) else: print(-1) if __name__ == "__main__": main() ```
output
1
15,380
22
30,761
Provide tags and a correct Python 3 solution for this coding contest problem. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1
instruction
0
15,381
22
30,762
Tags: brute force, number theory, sortings Correct Solution: ``` c=0; input(); l=sorted(map(int,input().split())) for i in l: if i%l[0]!=0:c=1;break print([-1,l[0]][c==0]) ```
output
1
15,381
22
30,763
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` n = int(input()) a = [int(i) for i in input().split()] m = min(a) f = 1 for i in a: if i % m != 0: print(-1) f = 0 break if f == 1: print(m) ```
instruction
0
15,382
22
30,764
Yes
output
1
15,382
22
30,765
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` n = int(input()) a = list(map(int, input().split())) a.sort() ans = True m = a[0] for i in range(1, n): if not(a[i]%m): continue else: print("-1") exit() print(m) ```
instruction
0
15,383
22
30,766
Yes
output
1
15,383
22
30,767
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` n=int(input()) l=list(map(int,input().split())) k=min(l) t=0 for i in range(n): if l[i]%k==0: t+=1 if t==n: print(k) else: print(-1) ```
instruction
0
15,384
22
30,768
Yes
output
1
15,384
22
30,769
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` garbage = int(input()) l = list(map(int, input().rstrip().split(" "))) m = min(l) r = m for i in l: if i%m !=0: r = -1 print(r) ```
instruction
0
15,385
22
30,770
Yes
output
1
15,385
22
30,771
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` from sys import stdin def read(): return map(int, stdin.readline().split()) read() a = list(read()) x = max(a) for y in a: if x % y != 0: x = -1 break print(x) ```
instruction
0
15,386
22
30,772
No
output
1
15,386
22
30,773
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` n = int(input()) A = input().split() k = min(A) p = 0 for i in range(n): if int(A[i]) % int(k) != 0: p = 1 break if p == 1: print(-1) else: print(k) ```
instruction
0
15,387
22
30,774
No
output
1
15,387
22
30,775
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` n = int(input().strip()) a = input().strip().split(' ') d = int(min(a)) div = True for i in a: if int(i) % d != 0: div = False break if div: print(d) else: print(-1) ```
instruction
0
15,388
22
30,776
No
output
1
15,388
22
30,777
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, consisting of n positive integers. Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! Input The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the array elements. Output Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1. If there are multiple answers, you are allowed to print any of them. Examples Input 3 2 2 4 Output 2 Input 5 2 1 3 1 6 Output 1 Input 3 2 3 5 Output -1 Submitted Solution: ``` import math n = input() s = list(map(int, input().split())) a = 0 for x in s: a = math.gcd(a, x) print(a) ```
instruction
0
15,389
22
30,778
No
output
1
15,389
22
30,779
Provide tags and a correct Python 3 solution for this coding contest problem. It's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points. Mashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way. Please, help him. Find n distinct integers a1, a2, ..., an such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 109. Input The first line of input contains two space-separated integers n, k (1 ≤ n ≤ 105; 0 ≤ k ≤ 108). Output If such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109). Examples Input 5 2 Output 1 2 3 4 5 Input 5 3 Output 2 4 3 7 1 Input 7 2 Output -1 Note gcd(x, y) is greatest common divisor of x and y.
instruction
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Tags: constructive algorithms, number theory Correct Solution: ``` #!/usr/bin/env python3 from sys import stdin MAXNUM = int(2e6) primes = list() isprime = [True for i in range(MAXNUM+1)] def getPrimes(): for i in range(2, MAXNUM+1): if isprime[i]: primes.append(i) j = i*i while j < MAXNUM+1: isprime[j] = False j += i def solve(tc): n, k = map(int, stdin.readline().split()) pairs = n//2 if pairs==0: if k==0: print(' '.join(map(lambda x: str(x), list(range(1,n+1))))) else: print(-1) return if pairs > k: print(-1) return getPrimes() remain = k - (pairs - 1) ans = list() ans.extend([remain, remain*2]) p = 0 while len(ans) < n: if primes[p] != remain and primes[p] != remain*2: ans.append(primes[p]) p += 1 print(' '.join(map(lambda x: str(x), ans))) tc = 1 solve(tc) ```
output
1
15,412
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30,825
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
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Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys from functools import lru_cache, cmp_to_key from heapq import merge, heapify, heappop, heappush from math import ceil, floor, gcd, fabs, factorial, fmod, sqrt, inf from collections import defaultdict as dd, deque, Counter as C from itertools import combinations as comb, permutations as perm from bisect import bisect_left as bl, bisect_right as br, bisect from time import perf_counter from fractions import Fraction # sys.setrecursionlimit(pow(10, 6)) # sys.stdin = open("input.txt", "r") # sys.stdout = open("output.txt", "w") mod = pow(10, 9) + 7 mod2 = 998244353 def data(): return sys.stdin.readline().strip() def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end) def l(): return list(sp()) def sl(): return list(ssp()) def sp(): return map(int, data().split()) def ssp(): return map(str, data().split()) def l1d(n, val=0): return [val for i in range(n)] def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)] def prime(number): if number == 2: return True if number & 1: i = 2 while i * i <= number: if number % i == 0: return False i += 1 return True return False arr = [] for i in range(2, 101): if prime(i): arr.append(i) if i * i <= 100: arr.append(i*i) arr.sort() low, high = 0, 24 c = 0 for i in range(20): out(arr[i]) sys.stdout.flush() verdict = data() if verdict.lower() == 'yes': c += 1 if c == 2: out("composite") exit() out("prime") ```
output
1
15,525
22
31,051
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
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15,526
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Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys def main(): a = [2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49] factors_count = 0 for i in a: print(i, flush=True) read = sys.stdin.readline().strip() if read == "yes": factors_count += 1 if factors_count > 1: break if factors_count>1: print("composite", flush=True) else: print("prime", flush=True) main() ```
output
1
15,526
22
31,053
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
0
15,527
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Tags: constructive algorithms, interactive, math Correct Solution: ``` import os import sys if os.path.exists('/mnt/c/Users/Square/square/codeforces'): f = iter(open('A.txt').readlines()) def input(): return next(f) input = lambda: sys.stdin.readline().strip() else: input = lambda: sys.stdin.readline().strip() def primes(n): A = [1] * (n+1) A[0] = A[1] = 1 primes = [] lenA = len(A) for i in range(2, lenA): if A[i] == 1: primes.append(i) for j in range(i*2, lenA, i): A[j] = 0 return primes # print(len(primes(50))) def main(): ps = primes(50) ps.extend([i**2 for i in primes(10)]) # print(len(ps)) r = 0 for p in ps: print(p, flush=True) if input() == 'yes': r += 1 if r <= 1: print('prime', flush=True) else: print('composite', flush=True) main() # return 'no' # print(main()) # l, r = 1, 10**6+1 # while l + 1 < r: # cur = (l + r) // 2 # print(cur, flush=True) # res = input() # if res == '>=': # l = cur # else: # r = cur # print('! %d' % l, flush=True) ```
output
1
15,527
22
31,055
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
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Tags: constructive algorithms, interactive, math Correct Solution: ``` import sys input = sys.stdin.readline flush = sys.stdout.flush def query(x): print(x) flush() y = input()[:-1] return 1 if y == "yes" else 0 A = [2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49] cnt = 0 for a in A: cnt += query(a) print("composite" if cnt >= 2 else "prime") ```
output
1
15,528
22
31,057
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
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Tags: constructive algorithms, interactive, math Correct Solution: ``` #------------------Important Modules------------------# from sys import stdin,stdout from bisect import bisect_left as bl from bisect import bisect_right as br from heapq import * from random import * from itertools import permutations input=stdin.readline prin=stdout.write from random import sample from collections import Counter,deque from fractions import * from math import sqrt,ceil,log2,gcd,cos,pi,floor from copy import deepcopy #dist=[0]*(n) mod=10**9+7 mod2=998244353 def ps(n): cp=0;lk=0;arr={} lk=0;ap=n cc=0 while n%2==0: n=n//2 cc=1 if cc==1: lk+=1 for ps in range(3,ceil(sqrt(n))+1,2): #print(ps) cc=0 while n%ps==0: n=n//ps cc=1 lk+=1 if cc==1 else 0 if n!=1: lk+=1 if lk==1: return False #print(arr) return True #count=0 #dp=[[0 for i in range(m)] for j in range(n)] #[int(x) for x in input().strip().split()] def gcd(x, y): while(y): x, y = y, x % y return x # Driver Code def factorials(n,r): #This calculates ncr mod 10**9+7 slr=n;dpr=r qlr=1;qs=1 mod=10**9+7 for ip in range(n-r+1,n): qlr=(qlr*ip)%mod for ij in range(1,r): qs=(qs*ij)%mod #print(qlr,qs) ans=(qlr*modInverse(qs))%mod return ans def modInverse(b): qr=10**9+7 return pow(b, qr - 2,qr) #=============================================================================================== ### START ITERATE RECURSION ### from types import GeneratorType def iterative(f, stack=[]): def wrapped_func(*args, **kwargs): if stack: return f(*args, **kwargs) to = f(*args, **kwargs) while True: if type(to) is GeneratorType: stack.append(to) to = next(to) continue stack.pop() if not stack: break to = stack[-1].send(to) return to return wrapped_func def power(arr): listrep = arr subsets = [] for i in range(2**len(listrep)): subset = [] for k in range(len(listrep)): if i & 1<<k: subset.append(listrep[k]) subsets.append(subset) return subsets def pda(n) : list=[];su=0 for i in range(1, int(sqrt(n) + 1)) : if (n % i == 0) : if (n // i == i) : list.append(i) su+=i else : list.append(n//i);list.append(i) su+=i;su+=n//i # The list will be printed in reverse return su def dis(xa,ya,xb,yb): return sqrt((xa-xb)**2+(ya-yb)**2) #### END ITERATE RECURSION #### #=============================================================================================== #----------Input functions--------------------# def ii(): return int(input()) def ilist(): return [int(x) for x in input().strip().split()] def islist(): return list(map(str,input().split().rstrip())) def inp(): return input().strip() def google(test): return "Case #"+str(test)+": "; def overlap(x1,y1,x2,y2): if x2>y1: return y1-x2 if y1>y2: return y2-x2 return y1-x2; ###-------------------------CODE STARTS HERE--------------------------------########### def dist(x1,y1,x2,y2): return sqrt((x1-x2)**2+(y1-y2)**2) def sieve(n): prime = [True for i in range(n + 1)] p = 2 while (p * p <= n): if (prime[p] == True): for i in range(p * 2, n + 1, p): prime[i] = False p += 1 prime[0]= False prime[1]= False ans=[] for i in range(1,n+1): if prime[i]: ans.append(i) return ans def prod(arr): n=len(arr) k=1 for j in range(n): k*=arr[j] return k def SumOfDigits(s): su=0 while (s): su+=s%10 s=s//10 return su ######################################################################################### #def valid(sec,hr,min,nano): #t=int(input()) t=1 ans=sieve(50) for i in ans: if i*i<50: ans.append(i*i) ans.sort() for pl in range(t): cc=1 co=0 #print(len(ans)) for query in ans: print(query) stdout.flush() result=inp() if result=="yes": co+=1 if co>=2: cc=0 break an="composite" if cc==0 else "prime" print(an);stdout.flush() ```
output
1
15,529
22
31,059
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
0
15,530
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Tags: constructive algorithms, interactive, math Correct Solution: ``` #Code by Sounak, IIESTS #------------------------------warmup---------------------------- import os import sys import math from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #-------------------game starts now----------------------------------------------------- a=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,4,9,25,49] n=len(a) count=0 for i in a: print(i) sys.stdout.flush() s=input() if s=="yes": count+=1 if count>=2: print("composite") else: print("prime") ```
output
1
15,530
22
31,061
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
0
15,531
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Tags: constructive algorithms, interactive, math Correct Solution: ``` #------------------------template--------------------------# import os import sys from math import * from collections import * # from fractions import * # from heapq import* from bisect import * from io import BytesIO, IOBase def vsInput(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") ALPHA='abcdefghijklmnopqrstuvwxyz' M=10**9+7 EPS=1e-6 def Ceil(a,b): return a//b+int(a%b>0) def value():return tuple(map(int,input().split())) def array():return [int(i) for i in input().split()] def Int():return int(input()) def Str():return input() def arrayS():return [i for i in input().split()] #-------------------------code---------------------------# # vsInput() def primeN(n): prime = [True for i in range(n+1)] prime[0]=False prime[1]=False p=2 while(p*p<=n): if(prime[p]): for i in range(p*p,n+1,p): prime[i]=False p+=1 return [p for p in range(n+1) if(prime[p])] primes=primeN(50) # print(primes) have={} have[2]=[37, 41, 43, 47] have[3]=[23, 29, 31] have[5]=[17, 19] have[7]=[11, 13] found=0 for i in [2,3,5,7]: print(i,flush=True) res=input() if(res=='yes'):found+=1 for p in have[i]: print(p,flush=True) res=input() if(res=='yes'):found+=1 print(i*i,flush=True) res=input() if(res=='yes'):found+=1 if(found>1): print("composite",flush=True) exit() print("prime",flush=True) exit() ```
output
1
15,531
22
31,063
Provide tags and a correct Python 3 solution for this coding contest problem. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).
instruction
0
15,532
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31,064
Tags: constructive algorithms, interactive, math Correct Solution: ``` import os import sys from io import BytesIO, IOBase import math from decimal import * from collections import defaultdict getcontext().prec = 25 MOD = pow(10, 9) + 7 BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # n, k = map(int, input().split(" ")) # = list(map(int, input().split(" "))) # for _ in range(int(input())): a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] ans = [] for i in range(15): print(a[i]) sys.stdout.flush() ans.append(input()) if ans.count("yes") > 1: print("composite") elif ans.count('yes') == 1: yes = 1 ind = 10 for i in range(4): if ans[i] == "yes": ind = a[i] break j = 2 while ind ** j < 101: print(ind ** j) sys.stdout.flush() if input() == "yes": yes += 1 break j+=1 if yes == 1: print('prime') else: print('composite') else: print('prime') ```
output
1
15,532
22
31,065
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` from sys import stdout, stdin PS = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] # PSL50 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] ## len == 15 # PSU50 = [53, 59, 61, 67, 71, 73, 79, 83, 89, 97] ## len == 10 def ask_and_yes( num): print(num) stdout.flush() ## get cpu answer line = stdin.readline().strip() return line == "yes" def solve(): # yes_cnt = 0 first_p = -1 for p in PS: if p >= 53: print("prime") return else: if ask_and_yes( p): first_p = p break ## rewind back quo = int(100/first_p) ## deal with edge cases if first_p >= quo: print( "prime") return ## get the first feasible prime for i in range( len( PS)-1, -1, -1): if PS[ i] < quo: break ## start questioning again for j in range( i, -1, -1): if PS[ j] == first_p: break ## fixed else: if ask_and_yes( PS[ j]): print( "composite") return ## one last time ## fixed if ask_and_yes( first_p*first_p): print( "composite") else: print( "prime") solve() ```
instruction
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31,066
Yes
output
1
15,533
22
31,067
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` import sys def is_prime(n, primes): for p in primes: if n % p == 0: return False else: return True def main(): primes = [2, 3, 5, 7] for i in range(primes[-1] + 2, 49, 2): if is_prime(i, primes): primes.append(i) ndivs = 0 last_divisor = -1 for p in primes[:4]: print(p) sys.stdout.flush() ans = sys.stdin.readline().strip() == "no" ndivs += not ans if not ans: last_divisor = p if ndivs >= 2: break if ndivs > 1: print("composite") elif ndivs == 0: print("prime") else: # ndivs == 1 print(last_divisor * last_divisor) sys.stdout.flush() ans = sys.stdin.readline().strip() == "no" if not ans: print("composite") else: for p in primes[4:]: print(p) sys.stdout.flush() ans = sys.stdin.readline().strip() == "no" if not ans: print("composite") break else: print("prime") sys.stdout.flush() if __name__ == "__main__": main() ```
instruction
0
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Yes
output
1
15,534
22
31,069
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` import os import sys if os.path.exists('/mnt/c/Users/Square/square/codeforces'): f = iter(open('A.txt').readlines()) def input(): return next(f) input = lambda: sys.stdin.readline().strip() else: input = lambda: sys.stdin.readline().strip() fprint = lambda *args: print(*args, flush=True) def primes(n): A = [1] * (n+1) A[0] = A[1] = 1 primes = [] lenA = len(A) for i in range(2, lenA): if A[i] == 1: primes.append(i) for j in range(i*2, lenA, i): A[j] = 0 return primes # print(len(primes(50))) def main(): ps = primes(50) ps.extend([i**2 for i in primes(10)]) # print(len(ps)) r = 0 for p in ps: fprint(p) if input() == 'yes': r += 1 if r <= 1: fprint('prime') else: fprint('composite') main() # return 'no' # print(main()) # l, r = 1, 10**6+1 # while l + 1 < r: # cur = (l + r) // 2 # print(cur, flush=True) # res = input() # if res == '>=': # l = cur # else: # r = cur # print('! %d' % l, flush=True) ```
instruction
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Yes
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1
15,535
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31,071
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` #------------------------template--------------------------# import os import sys from math import * from collections import * # from fractions import * # from heapq import* from bisect import * from io import BytesIO, IOBase def vsInput(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") ALPHA='abcdefghijklmnopqrstuvwxyz' M=10**9+7 EPS=1e-6 def Ceil(a,b): return a//b+int(a%b>0) def value():return tuple(map(int,input().split())) def array():return [int(i) for i in input().split()] def Int():return int(input()) def Str():return input() def arrayS():return [i for i in input().split()] #-------------------------code---------------------------# # vsInput() def primeN(n): prime = [True for i in range(n+1)] prime[0]=False prime[1]=False p=2 while(p*p<=n): if(prime[p]): for i in range(p*p,n+1,p): prime[i]=False p+=1 return [p for p in range(n+1) if(prime[p])] primes=primeN(50) found=0 for i in primes: print(i,flush=True) res=input() if(res=='yes'):found+=1 if(i>7):continue print(i*i,flush=True) res=input() if(res=='yes'):found+=1 if(found>1): print("composite",flush=True) else: print("prime",flush=True) exit() ```
instruction
0
15,536
22
31,072
Yes
output
1
15,536
22
31,073
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` from sys import stdout arr = [] for i in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]: print(i) stdout.flush() arr.append(input()) if arr.count('yes') > 1: print('composite') else: print('prime') ```
instruction
0
15,537
22
31,074
No
output
1
15,537
22
31,075
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` import sys from math import sqrt def pl(): l=[] for i in range(2,101): k=[] for j in range(2,int(sqrt(i))+1): if i%j==0: k+=[j] if (k==[]): l+=[i] return l def main(): k=pl() l=[] i=0 while i<20: print(k[i]) sys.stdout.flush() s=input() if s=='yes' and k[i]==2: print(4) sys.stdout.flush() j=input() if j=='yes': l+=[k[i],4] else: l+=[k[i]] i+=2 elif s=='yes' and k[i]==3: print(9) sys.stdout.flush() j=input() if j=='yes': l+=[k[i],9] else: l+=[k[i]] i+=2 elif s=='yes' and k[i]==5: print(25) sys.stdout.flush() j=input() if j=='yes': l+=[k[i],25] else: l+=[k[i]] i+=2 elif s=='yes' and k[i]==7: print(49) sys.stdout.flush() j=input() if j=='yes': l+=[k[i],49] else: l+=[k[i]] i+=2 elif s=='yes': l+=[k[i]] i+=1 elif s=='no': i+=1 continue if len(l)<=1: print('prime') sys.stdout.flush() else: print('composite') sys.stdout.flush if __name__=='__main__': main() ```
instruction
0
15,538
22
31,076
No
output
1
15,538
22
31,077
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` import os import sys if os.path.exists('/mnt/c/Users/Square/square/codeforces'): f = iter(open('A.txt').readlines()) def input(): return next(f) input = lambda: sys.stdin.readline().strip() else: input = lambda: sys.stdin.readline().strip() def primes(n): A = [1] * (n+1) A[0] = A[1] = 1 primes = [] lenA = len(A) for i in range(2, lenA): if A[i] == 1: primes.append(i) for j in range(i*2, lenA, i): A[j] = 0 return primes print(len(primes(50))) def main(): ps = primes(100) ps.append([i**2 for i in primes(10)]) r = 0 for p in ps: print(p, flush=True) if input() == 'yes': res += 1 if res <= 1: print('yes', flush=True) else: print('no', flush=True) # return 'no' # print(main()) # l, r = 1, 10**6+1 # while l + 1 < r: # cur = (l + r) // 2 # print(cur, flush=True) # res = input() # if res == '>=': # l = cur # else: # r = cur # print('! %d' % l, flush=True) ```
instruction
0
15,539
22
31,078
No
output
1
15,539
22
31,079
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is an interactive problem. In the output section below you will see the information about flushing the output. Bear Limak thinks of some hidden number — an integer from interval [2, 100]. Your task is to say if the hidden number is prime or composite. Integer x > 1 is called prime if it has exactly two distinct divisors, 1 and x. If integer x > 1 is not prime, it's called composite. You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no". For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14. When you are done asking queries, print "prime" or "composite" and terminate your program. You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2, 100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct. You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). Input After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. Output Up to 20 times you can ask a query — print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input. In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program. To flush you can use (just after printing an integer and end-of-line): * fflush(stdout) in C++; * System.out.flush() in Java; * stdout.flush() in Python; * flush(output) in Pascal; * See the documentation for other languages. Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100]. Of course, his/her solution won't be able to read the hidden number from the input. Examples Input yes no yes Output 2 80 5 composite Input no yes no no no Output 58 59 78 78 2 prime Note The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process. <image> The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30. <image> 59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). Submitted Solution: ``` primes = (2, 3, 5, 7, 11, 13, 17, 19, 23) count = 0 for p in primes: print(p) if input().strip() == "yes": count += 1 print(p * p) if input().strip() == "yes": count += 1 print("composite" if count >= 2 else "prime") ```
instruction
0
15,540
22
31,080
No
output
1
15,540
22
31,081
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,626
22
33,252
"Correct Solution: ``` a, b, k = map(int, input().split()) n = [] for i in range(1, 101): if a%i==0 and b%i==0: n.append(i) print(n[-k]) ```
output
1
16,626
22
33,253
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,627
22
33,254
"Correct Solution: ``` A,B,K=map(int,input().split()) List=[] for i in range (1,101): if A%i==0 and B%i==0: List.append(i) print(List[-K]) ```
output
1
16,627
22
33,255
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,628
22
33,256
"Correct Solution: ``` A, B, K = map(int, input().split()) m = [x for x in range(1, min(A, B)+1) if A%x==0 and B%x==0] print(m[-K]) ```
output
1
16,628
22
33,257
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,629
22
33,258
"Correct Solution: ``` A, B, K = map(int,input().split()) l = [x for x in range(1,A+1) if A%x == 0 and B%x == 0] print(l[-K]) ```
output
1
16,629
22
33,259
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,630
22
33,260
"Correct Solution: ``` a,b,k=[int(s) for s in input().split()] c=[] for i in range(1,101): if a%i==0 and b%i==0: c = c+[i] print(c[-k]) ```
output
1
16,630
22
33,261
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,631
22
33,262
"Correct Solution: ``` a,b,k=map(int,input().split()) list = [] for i in range(1,min(a,b)+1): if(a%i==0 and b%i==0): list.append(i) print(list[-k]) ```
output
1
16,631
22
33,263
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,632
22
33,264
"Correct Solution: ``` a,b,k=map(int,input().split()) print(list(filter(lambda x:a%x+b%x==0, [i for i in range(min(a,b),0,-1)]))[k-1]) ```
output
1
16,632
22
33,265
Provide a correct Python 3 solution for this coding contest problem. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1
instruction
0
16,633
22
33,266
"Correct Solution: ``` a,b,k=map(int,input().split()) l=[] for i in range(min(a,b),0,-1): if a%i==b%i==0: l.append(i) print(l[k-1]) ```
output
1
16,633
22
33,267
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1 Submitted Solution: ``` A, B, K = map(int, input().split()) div = [i for i in range(1, min(A, B) + 1) if A % i == 0 and B % i == 0] print(div[-K]) ```
instruction
0
16,634
22
33,268
Yes
output
1
16,634
22
33,269
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1 Submitted Solution: ``` a, b, k = map(int, input().split()) array = [i for i in range(1, 101) if a % i + b % i < 1] print(array[-k]) ```
instruction
0
16,635
22
33,270
Yes
output
1
16,635
22
33,271
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1 Submitted Solution: ``` A,B,K=map(int,input().split());print([i for i in range(A+1)if i>=1>A%i+B%i][::-1][K-1]) ```
instruction
0
16,636
22
33,272
Yes
output
1
16,636
22
33,273
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integers A and B. Find the K-th largest positive integer that divides both A and B. The input guarantees that there exists such a number. Constraints * All values in input are integers. * 1 \leq A, B \leq 100 * The K-th largest positive integer that divides both A and B exists. * K \geq 1 Input Input is given from Standard Input in the following format: A B K Output Print the K-th largest positive integer that divides both A and B. Examples Input 8 12 2 Output 2 Input 100 50 4 Output 5 Input 1 1 1 Output 1 Submitted Solution: ``` a,b,k=map(int,input().split()) i=101 c=0 while(c!=k): i-=1 if a%i==0 and b%i==0: c+=1 print(i) ```
instruction
0
16,637
22
33,274
Yes
output
1
16,637
22
33,275