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: Wrong Answer)

import java.util.Scanner;

public 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();
		
		int countA = 0;
		int countB = 0;
		int[] Ayaku = new int[A + 1];
		int[] Byaku = new int[B + 1];
		int[] yaku = new int[A + 1];
		
		for(int i = 1; i <= A; i++) {
			if(A % i == 0) {
				countA++;
				Ayaku[countA] = i;
			}
		}
		
		for(int i = 1; i <= B; i++) {
			if(B % i == 0) {
				countB++;
				Byaku[countB] = i;
			}
		}
		
		for(int i = 1; i <= countA; i++) {
			for(int j = 1; j <= countB; j++) {
				if(Ayaku[i] == Byaku[j]) {
					yaku[i] = Ayaku[i];
				}
			}
		}
		System.out.println(yaku[K]);
	}
}