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 Main2
{
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		
		int[][] ans = new int[n][4];
		
		for(int t=0; t<n; t++){
			ans[t][0] = (t*6)+1;
			ans[t][1] = ans[t][0] + 2;
			ans[t][2] = ans[t][1] + 1;
			ans[t][3] = ans[t][2] + 1;
		}
		
		System.out.println(ans[n-1][3]*k);
		for(int i=0; i<n; i++)
		{
			System.out.println((ans[i][0]*k)+ " " + (ans[i][1]*k) + " " + (ans[i][2]*k) + " " + (ans[i][3]*k));
		}
	}
}