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: Accepted)

import scipy as sp


def divisor(num):
    list = set()
    for i in sp.arange(1, num+1):
        if num % i == 0:
            list.add(i)
    return list


a, b, k = [int(i) for i in input().split()]

div_a = divisor(a)
div_b = divisor(b)

cd = sp.sort(list(div_a & div_b))
cd_r = cd[::-1]
print(cd_r[k-1])