message stringlengths 2 57.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
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 | 14,760 | 22 | 29,520 |
"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 | 0 | 15,412 | 22 | 30,824 |
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 | 22 | 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 | 0 | 15,525 | 22 | 31,050 |
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 | 0 | 15,526 | 22 | 31,052 |
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 | 22 | 31,054 |
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 | 0 | 15,528 | 22 | 31,056 |
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 | 0 | 15,529 | 22 | 31,058 |
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 | 22 | 31,060 |
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 | 22 | 31,062 |
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 | 22 | 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 | 0 | 15,533 | 22 | 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 | 15,534 | 22 | 31,068 |
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 | 0 | 15,535 | 22 | 31,070 |
Yes | output | 1 | 15,535 | 22 | 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 |
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