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,"%d %d %d",$A,$B,$K);

// if ($A % 割り切る整数 == 0 || $B % 割り切れる整数==0) {
// }

for ($i = 100; $i >= 1 ; $i--) {
// A % $i -> Aを $iで割ったあまり
if ($A % $i == 0 && $B % $i == 0) {
    // echo $i . " \n";
    if ($i == $K) {
        echo $i;
    }
 }
}