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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>

int main(){
    
    int a, b, k;
    std::vector<int> ans;

    std::cin >> a >> b >> k;

    for(int i = 1; i <= 100; i++){
        if(a % i == 0 && b % i == 0) ans.emplace_back(i);
    }

    std::sort(ans.begin(), ans.end(), std::greater<int>());

    std::cout << ans[k - 1] << std::endl;
    
    return 0;
}