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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
#define endl "\n"

const int MOD = 1000000007;
int main()
{
	ios::sync_with_stdio(false);
  	cin.tie(0);
	
	int a, b, c;
	cin >> a  >> b >> c;
	vector<int> v;
	
	for(int i = 1; i <= b ; i++){
		if(a % i == 0 && b %  i == 0){
			v.push_back(i);
		}
	}
	sort(v.begin(),v.end());
	cout << v[c-1] << endl;
	
	
	
	
	return 0;
}