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);

// A, Bの約数を全て挙げる
// 共通のものにしぼる
// そのうちK番目のものをとってくる

$aArray = [];
for($i = 1; $i <= $A; $i++){
    if($A % $i === 0){
        $aArray[] = $i;
    }
}

$bArray = [];
for($i = 1; $i <= $B; $i++){
    if($B % $i === 0){
        $bArray[] = $i;
    }
}

$array = array_intersect($aArray, $bArray);
rsort($array);

$ans = $array[$K - 1];

echo $ans.PHP_EOL;