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 <array>
#include <deque>
#include <stack>
#include <queue>
#include <list>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <utility>
#include <cmath>
#include <iomanip>

using namespace std;
using ll=long long int;

int main() {
    int a, b, k;
    cin >> a >> b >> k;

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

    cout << conf[conf.size()-k] << endl;

    return 0;
}