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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws Exception {

    	try(BufferedReader r = new BufferedReader(new InputStreamReader(System.in))){

    		String line = r.readLine();
    		String[] vals = line.split(" ");

    		int A = Integer.parseInt(vals[0]);
    		int B = Integer.parseInt(vals[1]);
    		int K = Integer.parseInt(vals[2]);
	    	int cnt = 0;

	    	int small = Math.min(A, B);
	    	for(int i=small; i>=1; i--) {

	    		if(A % i == 0 && B % i == 0){
	    			if(++cnt == K) {
	    				System.out.println(i);
	    				return;
	    			}
	    		}
	    	}
    	}
    }
}