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: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
using namespace std;
using ll = long long;
const double PI = 3.14159265358979323846;

int main() {
  int a, b, k;
  cin >> a >> b >> k;
  queue<int> d;
  for(int i = min(a, b); i >= 1; i--) {
    if(a % i == 0 && b % i == 0) {
      d.push(i);
    }
  }
  for(int i = 0; i < k - 1; i++) {
    d.pop();
  }
  cout << d.front() << endl;
}