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 12.16.1) (judge verdict: Wrong Answer)

function main(input) {
  const args = input.split(' ').map(n => parseInt(n, 10));
  const A = args[0],
        B = args[1],
        K = args[2];
  let cnt = 0;
  
  for (let i = 1; i <= 100; i++) {
    if (A % i === 0 && B % i === 0) {
      cnt++;
      if (cnt === K) {
        console.log(i);
        break;
      }
    }
  }
}

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