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 (3.4.3) (judge verdict: Wrong Answer)

def factorize(n):
    n_list = []
    for i in range(n):
        x = i + 1
        if n % x == 0:
            n_list.append(x)
    return n_list


if __name__ == '__main__':
    A, B, C = input().split()
    a_list = factorize(int(A))
    b_list = factorize(int(B))
    and_list = list(set(a_list) & set(b_list))
    and_list.reverse()
    print(and_list[int(C) - 1])