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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
public class Main {

	public void run() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();
		List<Integer> arrayData = new ArrayList<Integer>();
		String[] lineArray = line.split(" ");
		for (String token : lineArray) {
			arrayData.add(Integer.parseInt(token));
		}
		int A = arrayData.get(0);
		int B = arrayData.get(1);
		int K = arrayData.get(2);
		List<Integer> li = new ArrayList<Integer>();
		int smaller = Math.min(A, B);
		for(int i=1; i<=smaller;i++){
	
				if(A%i == 0 && B%i == 0){
					li.add(i);
				}

		}
		
		Collections.reverse(li);
		System.out.println(li.get(K-1));
	}
    public static void main(String[] args) throws Exception {
        new Main().run();
    }

}