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.ArrayList;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		try {
			Scanner scanner = new Scanner(System.in);

			int A = scanner.nextInt();
			int B = scanner.nextInt();
			int K = scanner.nextInt();

			List<Integer> answerList = new ArrayList<>();

			int loopCountMax = A > B ? B : A;

			for (int i = 1; i < loopCountMax; i++) {
				if (A % i == 0 && B % i == 0) answerList.add(i);
			}

			System.out.println(answerList.get(K - 1));
			scanner.close();
		} catch (InputMismatchException e) {
			System.out.println("整数を入力してください。");
		}
	}
}