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() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int a,b,k;
	cin>>a>>b>>k;
	vector<int>	v;
	for(int i=min(a,b); i>0; i--) {
		if(a%i==0&&b%i==0) {
			v.push_back(i);
		}
	}
	cout<<v[k-1]<<endl;
	return 0;
}