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 PyPy3 (2.4.0) (judge verdict: Accepted)

def gcd(a, b):
    a, b = max(a, b), min(a, b)
    if b == 0:
        return a
    return gcd(b, a % b)


def main():
    A, B, K = map(int, input().split())
    C = gcd(A, B)
    divs = [1, C]
    i = 2
    while i**2 <= C:
        if C % i == 0:
            divs.append(i)
            if C // i != i:
                divs.append(C//i)
        i += 1
    divs.sort(reverse=True)
    print(divs[K-1])


if __name__ == "__main__":
    main()