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: Runtime Error)

// Atcoder120 - B
function divisor(n) {var ret=[]; for (var i=1;i*i<=n;i++){if(n%i==0){ret.push(i);if(i*i!=n)ret.push(n/i);}}return ret;}
function gcd(a,b){if(b>a){var temp=a; a=b; b=temp;} var r=a%b; while(r!=0){a=b; b=r; r=a%b;} return b;}
function main(input) {
  var inputs = input.split('\n');
  var a, b, k;
  [a, b, k] = inputs[0].split(' ');

  var aDivisors = divisor(a);
  var bDivisors = divisor(b);

  var counter = 0;
  var kthCd = 0;
  aDivisors.sort((i, j) => i - j).some((item) => {
    counter += bDivisors.indexOf(item) >= 0 ? 1 : 0;
    if (counter == k) {
      kthCd = item;
      return true;
    }
  });

  console.log(kthCd);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));