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.*;

import javax.swing.text.AbstractDocument.BranchElement;

import com.sun.org.apache.xpath.internal.SourceTree;

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();
        Set<Integer> ans1 = new TreeSet<>();
        for (int i = 1; i <= a; i++) {
            if (a % i == 0) {
                ans1.add(i);
            }
        }
        Set<Integer> ans2 = new TreeSet<>();
        for (int i = 1; i <= b; i++) {
            if (b % i == 0) {
                ans2.add(i);
            }
        }
        List<Integer> result = new ArrayList<>();
        for (Integer val1 : ans1) {
            for (Integer val2 : ans2) {
                if (val1 == val2) {
                    result.add(val1);
                }
                if (val1 <= val2) {
                    break;
                }
            }
        }
        System.out.println(result.get(result.size() - k));
    }
}