Problem: Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.

Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.

Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.

Input

The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).

Output

On the first line print a single integer — the minimal possible m. 

On each of the next n lines print four space separated integers representing the i-th set.

Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.

Examples

Input

1 1


Output

5
1 2 3 5


Input

2 2


Output

22
2 4 6 22
14 18 10 16

Note

For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.

Solution (in JAVA):

Solution:
import java.util.*;

public class D {
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int k = scan.nextInt();
		int m = 6*n*k - k;
		System.out.println(m);
		for (int i = 1; i < n; i++){
			System.out.print((6*i*k - 5*k) + " ");
			System.out.print((6*i*k - 4*k) + " ");
			System.out.print((6*i*k - 3*k) + " ");
			System.out.print((6*i*k - 1*k));
			System.out.println();
		}
		System.out.print((6*n*k - 5*k) + " ");
		System.out.print((6*n*k - 4*k) + " ");
		System.out.print((6*n*k - 3*k) + " ");
		System.out.print((6*n*k - 1*k));
	}
}