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)

#include <iostream>
#include <vector>
#include <algorithm>
 
using namespace std;
 
int main() {
  int a,b,k;
  cin >> a >> b >> k;
  
  int ma, mb;
  
  if (a > b){
    ma = a;
    mb = b;
  } else {
    ma = b;
    mb = a;
  }
  
  vector<int> v;
  long long c[ma];
  long long count=0;
  for (int i=1;i<=ma;i++){
    if((ma%i==0) && (mb%i==0)){
      v.push_back(i);
      //count = count + 1;
    }
  }
  cout << v[v.size()-k] << endl;
  return 0;
}