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.Collections;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		// 整数の入力
		int a = sc.nextInt();
		int b = sc.nextInt();
		int k = sc.nextInt();
		ArrayList<Integer> aList = new ArrayList<Integer>();
		ArrayList<Integer> bList = new ArrayList<Integer>();
		ArrayList<Integer> ansList = new ArrayList<Integer>();

		for (int i = 1; i <= a; i++) {
			if (a % i == 0) {
				aList.add(i);
			}
		}

		for (int i = 1; i <= b; i++) {
			if (b % i == 0) {
				bList.add(i);
			}
		}

		if(aList.size() > bList.size()){
			for (int val : aList) {
				if(bList.contains(val)){
					ansList.add(val);
				}
			}
		}else{
			for (int val : bList) {
				if(aList.contains(val)){
					ansList.add(val);
				}
			}
		}

		Collections.sort(ansList, Collections.reverseOrder());
		System.out.println(ansList.get(k - 1));

		sc.close();
	}
}