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)

#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#define fi first
#define se second
#define pb push_back

using namespace std;
const long long MOD = (long long)1e9 + 7;

int a, b, k;
vector<int> vec;
int main()
{
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cin >> a >> b >> k;
	int x = min(a, b);
	for (int i = 1; i <= x; i++) {
		if (b%i || a % i) continue;
		vec.pb(i);
	}
	reverse(vec.begin(), vec.end());
	cout << vec[k - 1] << "\n";
	//system("pause");
	return 0;
}