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: Runtime Error)

#include <bits/stdc++.h>
#define rep(i,n) for(long long int i = 0; i < n; i++)
#define _rep(i,m,n) for(long long int i = m; i < n; i++)
#define print(n) std::cout << n << std::endl
#define _print(n) std::cout << n
using namespace std;
typedef long long ll;
const int N = 1000000;
const ll mod = 1000000007;

int main() {
    int a,b,k; cin >> a >> b >> k;
    vector<int> c;
    _rep(i,1,max(a,b)){
        if(a % i == 0 && b % i == 0)c.push_back(i);
    }
    print(c[c.size() - k]);
}