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: Runtime Error)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
  ios_base::sync_with_stdio(false);

  int a, b, k;
  cin >> a >> b >> k;
  vector <int> Div;
  int x = min(a,b), y = max(a,b);
  for (int i = 1; i < x ; i++)
    if ( !(x % i) && !(y % i))
      Div.push_back(i);  
  
  cout << Div[Div.size() - k] << endl;
}