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: Runtime Error)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();;
        int b = sc.nextInt();;
        int c = sc.nextInt();
        sc.close();
        Integer[] divisors = new Integer[Math.max(a, b)];
        Arrays.fill(divisors, 0);
        for (int i = 1; i <= Math.max(a, b); i++) {
            if (a % i == 0 && b % i == 0) divisors[i] = i;
        }
        Arrays.sort(divisors, Comparator.reverseOrder());
        System.out.println(divisors[c-1]);
    }
}