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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <numeric>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <string>
using namespace std;
#define lli long long int
#define MAX 100000000
int main()
{
    //cin.tie(0);
    //ios::sync_with_stdio(false);
    int A, B, K;
    cin >> A >> B >> K;
    vector<int> answer;
    int test = 1;
    while (answer.size() != K)
    {
        if ((A % test == 0) && (B % test == 0))
        {
            answer.push_back(test);
        }
        test++;
    }
    cout << answer[K - 1] << endl;
    return 0;
}