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.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();

		int cnt = 0;
		int ans = 100;

		while (true) {
			if (a % ans == 0 && b % ans == 0) {
				cnt++;
			}
			if (cnt == k) {
				break;
			}
			ans--;
			if (ans < 0) {
				break;
			}
		}

		System.out.println(ans);

		sc.close();
	}
}