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 REP(i, n) for (int i = 0; i < (n); ++i)

#include <algorithm>
#include <iostream>
#include <vector>

using namespace std;

// int gcd(int a ,int b) {
//     return (b == 1) ? a : gcd(b, a % b);
// }

signed main() {
  ios::sync_with_stdio(false);
  long long a, b, k;
  cin >> a >> b >> k;
  int ans = 1000;
  for(int i=100;k;i--) {
    if(a % i == 0 && b % i == 0) {
        ans = i;
        k--;
    }
  }
  cout << ans << endl;
  return 0;
}