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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict';
console.log(function(args){
  const _tmp = args.trim().split(' ');
  const A = _tmp[0]|0, B = _tmp[1]|0;
  let K = _tmp[2]|0;
  const divisor = [];
  for ( let i = A; i >= 1; i-- ) {
    if ( A%i === 0 ) divisor.push(i);
  }
  for ( let j of divisor ) {
    if ( B%j === 0 && --K === 0 ) return j.toString();
  }
  return '1';
}(require('fs').readFileSync('/dev/stdin', 'utf8')));