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: Wrong Answer)

<?php
fscanf(STDIN, "%d %d %d", $a, $b, $k);
$a_div = [];
$b_div = [];
$ab_div = [];
for($i = 1; $i <= $a; $i++){
    if($a%$i == 0){
        $a_div[] = $i;
    }
}
for($i = 1; $i <= $b; $i++){
    if($b%$i == 0){
        $b_div[] = $i;
    }
}
$a_count = count($a_div);
$b_count = count($b_div);
for($i = 0; $i < $a_count; $i++){
    for($j = 0; $j < $b_count; $j++){
        if($a_div[$i] == $b_div[$j]){
            $ab_div[] = $a_div[$i];
        }
    }
}

echo $ab_div[$k-1];
?>