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
fscanf(STDIN, "%d %d %d",$a,$b,$k);
$a_divisor = array();
$b_divisor = array();
$com_divisor = array();
//aの約数を取得
for($i=1;$i<=$a;$i++){
	
	if($a % $i == 0){
			$a_divisor[] = $i;
	}
}
//ｂの約数を取得
for($i=1;$i<=$b;$i++){
	
	if($b % $i == 0){
		$b_divisor[] = $i;
	}
}
//aとbの公約数
for($i=0;$i<count($a_divisor);$i++){
	
	for($n=0;$n<count($b_divisor);$n++){
		
		if ($a_divisor[$i]==$b_divisor[$n]){
			
			$com_divisor[]=$a_divisor[$i];
			break;
		}
	}
}
//k番目に大きいもの
echo $com_divisor[count($com_divisor) - $k];
?>