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;
import java.util.ArrayList;

public class Main {
    public static void main(String args[]) throws Exception{
        BufferedReader stdR = new BufferedReader(new InputStreamReader(System.in));
        String[] str = stdR.readLine().split(" ");
        int A = Integer.parseInt(str[0]);
        int B = Integer.parseInt(str[1]);
        int K = Integer.parseInt(str[2]);
        int num = 1;
        int count = 0;
        ArrayList<Integer> ast = new ArrayList<Integer>();
        while(num <= Math.min(A, B)) {
            if(A % num == 0 && B % num == 0) {
                ast.add(num);
            }
            num++;
        }
        System.out.println(ast.get(ast.size() - K));
    }
}