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++ (GCC 9.2.1) (judge verdict: Accepted)

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

int main(){
    int a, b, k;
    cin >> a >> b >> k;
    vector<int> data(b);
    int j = 0;
    for (int i = 1; i < a+1; i++){
        if(a % i == 0 && b % i == 0){
            data.at(j) = i;
            j++;
        }
    }
    sort(data.begin(), data.end());//小さい順に並べる
    reverse(data.begin(), data.end());//リバース
    cout << data.at(k-1) << endl;
}