Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Python (3.8.2) (judge verdict: Accepted)

import sys
input = lambda: sys.stdin.readline().rstrip()

def main():
    a, b, k = map(int, input().split())
    cnt = 0
    for i in range(min(a,b), 0, -1):
        if a%i==0 and b%i==0:
            cnt += 1
        if cnt == k:
            print(i)
            return
        
if __name__ == '__main__':
    main()