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.*;

public class Main {
    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int a = Integer.parseInt(s.next());
        int b = Integer.parseInt(s.next());
        int k = Integer.parseInt(s.next());

        int min = a < b ? a : b;
        List<Integer> list = new ArrayList<Integer>();
        for (int i = 1; i <= min; i++) {
            if (a % i == 0 && b % i == 0) {
                list.add(i);
            }
        }
        Optional<Integer> an = list.stream()
                .sorted(Comparator.reverseOrder())
                .skip(k - 1)
                .findFirst();

        System.out.println(an.orElse(0));
    }
}