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: Runtime Error)

import java.util.*;
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();
      
		ArrayList<Integer> al = new ArrayList<>();

      	int min = A;
      	if(A>B){
          min = B;
        }
      
      	for(int i = 1; i < min+1; i++){
          	if((A%i==0)&&(B%i==0)){
              al.add(i);
            }
        }
      
		System.out.println(al.get((al.size()-K+1)));
	}
}