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 (5.6.30) (judge verdict: Accepted)

<?php
fscanf(STDIN,'%d %d %d',$A,$B,$K);
$max = max($A,$B);
$array = [];
for ($i=1; $i <= $max ; $i++) {
  // code...
  if($A%$i==0 && $B%$i==0){
    $array[] = $i;
  }
}
$arrayREV = array_reverse($array);
echo $arrayREV[$K-1];
 ?>