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: Wrong Answer)

import java.util.Scanner;
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();
	        int cnt = 0;
	        int ans = 0;
	        
	        for(int i=100; i>1; i--){
	        	if(A % i == 0){
	        		if(B % i == 0){
	        			cnt = cnt +1;
	        			if (K == cnt){
	        				ans = i;
	        				break;
	        			}
	        		}
	        	}
	        }
	        System.out.println(ans);
	}
}