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

$input = explode(' ', trim(fgets(STDIN)));
$a = (int)$input[0];
$b = (int)$input[1];
$k = (int)$input[2];

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