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.*;

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();
		List<Integer> a = new ArrayList<Integer>();
		for (int i=1;i<=100;i++) {
			if (A%i==0) {
				a.add(i);
			}
		}
		List<Integer> b = new ArrayList<Integer>();
		for (int i=1;i<=100;i++) {
			if (B%i==0) {
				b.add(i);
			}
		}
		List<Integer> c = new ArrayList<Integer>();
		for (int i=0;i<a.size();i++){
			if (b.contains(a.get(i))) {
				c.add(a.get(i));
			}
		}
		System.out.println(c.get(c.size()-K));
	}
}