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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

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

if ($a == 1 || $b ==1) {
	echo 1, PHP_EOL;
    exit();
}

$array = [];
$grater = $a < $b ? $a : $b;
while ($grater > 1) {
	if ($a % $grater === 0 && $b % $grater ===0) {
    	$array[] = $grater;
    }
    $grater--;
}

echo $array[$kth - 1], PHP_EOL;