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: Accepted)

<?php
// Your code here!
$input = explode(" ",trim(fgets(STDIN)));
$A = $input[0];
$B = $input[1];
$K = $input[2];

if ($A > $B) {
    $limit = $B;
} else {
    $limit = $A;
}

for ($i = 1; $i <= $limit; $i++) {
    if ($B % $i == 0 && $A % $i == 0) {
        $answer[] = $i;
    }
}

rsort($answer);
echo $answer[$K - 1];
?>