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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        
        Scanner scanner = new Scanner(System.in);
        int A = scanner.nextInt();
        int B = scanner.nextInt();
        int K = scanner.nextInt();
        int count = 0;
        
        List<Integer> list = new ArrayList<Integer>();
        for(int i=1; i<=100; i++){
            if(A%i==0 && B%i==0){
                list.add(i);
                count++;
            }
        }
        
        Collections.sort(list, Collections.reverseOrder());
        
        System.out.println(list.get(K-1));
        
    }
}