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, $k) = explode(' ', trim(fgets(STDIN)));

if ($k === 1) {
    echo 1, PHP_EOL;
    exit;
}

$x = [1];
for ($i = 2 ; $i <= 100; $i++) {
    if ($a % $i === 0 && $b % $i ===0) {
        $x[] = $i;
        if (count($x) === $k) {
            echo $i, PHP_EOL;
            exit();
        }
    }
}

echo ($x[$k - 1]), PHP_EOL;