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<iostream>
using namespace std;

int main(){
  int A, B, K, M;
  
  cin >> A >> B >> K;
  
  if(A > B){
    M = B;
  }
  else{
    M = A;
  }
  
  int a[100] = {};
  int k = 0;
  
  for(int i = 1; i <= M; i++){
    if(A % i == 0 && B % i == 0){
      a[k] = i;
      k += 1;
    }
  }
  
  cout << a[K-1] << endl;
  
  return 0;
}