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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
#define rep(i, n) for (int(i) = 0; (i) < (n); (i)++)
#define debug(x) cerr << #x << ": " << x << '\n'

int main()
{
    int A, B, K;
    cin >> A >> B >> K;
    if (A > B)
    {
        swap(A, B);
    }
    vector<int> ans;
    rep(i, A + 1)
    {
        if (i != 0 && A % i == 0 && B % i == 0)
        {
            ans.push_back(i);
        }
    }
    reverse(ans.begin(), ans.end());
    cout << ans[K - 1] << endl;
}