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 <string>
#include <algorithm>
#include <cmath>
typedef long long ll;
using namespace std;

int main()
{
    int a, b, k;
    cin >> a >> b >> k;
    int ans;
    int x;
    int cnt = 0;
    for (int i = 100; i >= 1; i--){
        x = i;
        if(a % x == 0 && b % x == 0) {
            ans = x;
            cnt++;
            if (cnt == k) break;
        }
    }
    cout << ans << endl;
    return 0;
}