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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

int main(int argc, const char *argv[]) {
  int a, b, k;
  cin >> a >> b >> k;

  int cnt = 0, ans;
  for (int i = 1; i <= max(a, b); ++i) {
    if (a % i == 0 && b % i == 0) {
      cnt++;

      if (cnt == k) {
        ans = i;
        break;
      }
    }
  }

  cout << ans << '\n';
  return 0;
}