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 <bits/stdc++.h>
using namespace std;

int main () {
  int a, b, K;
  cin >> a >> b >> K;
  int count = 0;
  if (a > b) {
   for (int i = b; i >= 1; i--) {
    if ((a%i == 0) && (b%i == 0)) count ++;
    if (count == K){
      cout << i << endl;
      break;
    }
   }
  }
  else{
   for (int i = a; i >= 1; i--) {
    if ((a%i == 0) && (b%i == 0)) count ++;
    if (count == K){
      cout << i << endl;
      break;
    }
   }
  }
}