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)

function main(input) {
  const args = input.split(' ');
  var A = Number(args[0]);
  var B = Number(args[1]);
  var K = Number(args[2]);
  var cu = 0;
  var sum;
  var count = 0;
  for (cu = A; cu > 0; --cu) {
    if (Number.isInteger(A / cu) && Number.isInteger(B / cu)) {
      count++;
      if (count === K) {
        sum = cu;
        break;
      }
    }
  }
  console.log(sum);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));