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: Wrong Answer)

function Main(input) {
  input = input.split(" ");
  var a = input[0];
  var b = input[1];
  var k = input[2];
  if(k == 1) {
    console.log(1);
    return false;
  }
  
  var ary = [1];
  for(var i = 2; i < 101; i++ ) {    
    if( a%i === 0 && b%i === 0 ) {
      ary.push(i);
      if(ary.length == k) {
        console.log(ary[k - 1]);
        return false;
      }
    }

  }
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));