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;



int main() {
    

    int A;
    int B;
    int K;
    cin >> A >> B >> K;
    int num = 0;
    vector<int> vec(max(A,B));
    for(int p =1; p<max(A,B)+1; p++){
    if(A%p == 0  &&  B%p == 0){
        vec.at(num) = p;
        num++;
    }}
    sort(vec.begin(), vec.end());
    reverse(vec.begin(), vec.end());
    cout << vec.at(K-1) << endl;

}