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.Scanner;


public class Main{

    public static void main(String []args){
       Scanner scan = new Scanner(System.in);
       int A = scan.nextInt();
       int B = scan.nextInt();
       int K = scan.nextInt();

        int count = 0;
        int ans = 0;

        int N = 0;
        
        for(int i=1; i<=Math.min(A,B); i++){
            if(A%i ==0 && B%i==0){
                N += 1;
            }
        }

        K = N-K+1;

        for(int i=1; count<K; i++){
            if(A%i ==0 && B%i==0){
                ans = i;
                count += 1;
            }
        }
        System.out.println(ans);
   
       scan.close();
    }
}