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)

function main(input) {
  const args = input.split(' ');
  const A = Number(args[0]);
  const B = Number(args[1]);
  const K = Number(args[2]);
  const [min, max] = A < B ? [A, B] : [B, A];
  const result = Array.from(Array(min), (v, i) => i + 1).reduce((sum, cu) => {
    if (Number.isInteger(min / cu) && Number.isInteger(max / cu)) {
      return [...sum, cu];
    }
    return sum;
  }, []);
  console.log(result.splice(result.length - K, 1)[0]);
}