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 sc = new Scanner(System.in);
        int numA = sc.nextInt();
        int numB = sc.nextInt();
        int numC = sc.nextInt();
        List<Integer> numAList = getNums(numA);
        List<Integer> numBList = getNums(numB);

        List<Integer> commonList = new ArrayList<>();
        for (int num : numAList) {
            if (numBList.contains(num)) {
                commonList.add(num);
            }
        }
        commonList.sort(Comparator.reverseOrder());
        System.out.println(commonList.get(numC- 1));
    }

    public static List<Integer> getNums(int num) {
        List<Integer> numList = new LinkedList<>();
        for (int n = 1; n <= num; n++) {
            if (num % n == 0) {
                numList.add(n);
            }
        }
        return numList;
    }
}