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.io.*;
import java.util.*;
public class test
{
    public static void main(String args[])
    {
        //System.out.println("Welcome");
        inputs in=new inputs(System.in);
        int n=in.nextInt(),k=in.nextInt();
        
        out(""+((n*6-1)*k));
        
        for(int i=0;i<n;i++)
        {
            int c=i*6;
            out(""+(c+1)*k+" "+(c+2)*k+" "+(c+3)*k+" "+(c+5)*k);
        }
    }
    
    static void out(String s)
    {
        System.out.println(s);
    }
}

class inputs
{
    public BufferedReader reader;
    public StringTokenizer token;
    
    inputs(InputStream str)
    {
        reader=new BufferedReader(new InputStreamReader(str));
        token=null;
    }
    
    int nextInt()
    {
        while(token==null||!token.hasMoreTokens())
        {
            try { token=new StringTokenizer(reader.readLine());   }
            catch(IOException e){  throw new RuntimeException(e); }
        }
        return Integer.parseInt(token.nextToken());
    }
    
    String next()
    {
        while(token==null||!token.hasMoreTokens())
        {
            try { token=new StringTokenizer(reader.readLine());   }
            catch(IOException e){  throw new RuntimeException(e); }
        }
        return token.nextToken();
    }
    
}