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
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($A,$B,$K) =  explode(" ",trim(fgets(STDIN)));
//$A = explode(" ",trim(fgets(STDIN)));

$resutl=array();
for($i=1;$i<=max($A,$B);$i++) {
  if ((($A % $i)==0) && (($B % $i)==0)) {
    $result[]=$i;
  }
}
rsort($result);
printf("%d\n",$result[$K-1]);