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 sc = new Scanner(System.in);
    	// 入力
    	int a = sc.nextInt();
    	int b = sc.nextInt();
    	int k = sc.nextInt();
    	int i = 0;
    	int cnt=0;

    	for(i = Math.min(a,b); i > 0; i--){
    		if(a % i == 0){
    			if(b % i == 0){
    				cnt++;
    				if(cnt == k){
    					break;
    				}
    			}
    		}
    	}


    	// 出力
    	System.out.println(i);
    }
}