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: Accepted)

<?php
fscanf(STDIN, '%d %d %d', $a, $b, $k);
$cnt = 0;
for ($i = min($a, $b); $i >= 1; $i--) {
    if ($a % $i === 0 && $b % $i === 0) {
        $cnt++;
        if ($cnt === $k) {
            $ans = $i;
            break;
        }
    }
}
echo $ans . PHP_EOL;