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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($a, $b, $k) = explode(" ", trim(fgets(STDIN)));

  $count =0;
  for($i=100; $i>=0; $i--){
    if($a % $i == 0 && $b % $i == 0){
      $count++;
    }
    if($count == $k){
      echo $i;
      exit;
    }
  }