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: Wrong Answer)

<?php 
  
//fscanf(STDIN,"%s%s",$s,$t);
fscanf(STDIN,"%s",$s);

$len=strlen($s);
$alive=array();
$alive[0]=$s[0];
$c=0;
for($i=1;$i<$len;$i++){
  if(end($alive)==$s[$i] || count($alive)==0){
    $alive[]=$s[$i];
   }else{
    $c++;
    array_pop($alive);
  }
}

echo ($c*2)."\n";