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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        int A = sc.nextInt();
        int B = sc.nextInt();
        int K = sc.nextInt();
        ArrayList<Integer> commonDivisors = new ArrayList<>();
        int idx = Math.min(A, B);

        for (int i = idx; i > 0; i--) {
            if (A % i == 0 && B % i == 0) {
                commonDivisors.add(i);
                if (commonDivisors.size() == K) {
                    break;
                }
            }
        }

        System.out.println(commonDivisors.get(K - 1));
    }

}