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.Scanner;
public class Main {
	public static void main(String [] args) {
		Scanner in = new Scanner(System.in);
		
		int a = in.nextInt();
		int b = in.nextInt();
		int k = in.nextInt();
		ArrayList<Integer> ks = new ArrayList<>();
		for(int i=1;i<=Math.min(a, b);i++) {
			if(a%i==0&&b%i==0) {
				ks.add(i);
				
				}
			}
		System.out.println(ks.get(ks.size()-k));
		}
	
		
	}