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.Scanner;
public class cfProblem {
    public static void main (String [] args) {
        Scanner s = new Scanner(System.in);
        long n = s.nextLong();
        long k = s.nextLong();
        long m = n*6 - 1;
        long ans=  m*k;
        System.out.println(ans);
        for (int i = 0; i < n; i++){
            long cur = i*6 + 1;
            long even = cur + 1;
            if (cur %3 != 0) even += 2;
            System.out.print(cur*k);
            System.out.print(" ");
            System.out.print((cur+2)*k);
            System.out.print(" ");
            System.out.print((cur+4)*k);
            System.out.print(" ");
            System.out.print(even*k);
            System.out.println();
        }
    }
}