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.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class B {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        
        StringTokenizer st = new StringTokenizer(bf.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        
        /*
        boolean[] primes = new boolean[104729];
        for(int i=0; i<primes.length; i++) {
            if(i % 2 == 0 || i % 3 == 0 || i % 5 == 0 || i % 7 == 0 || i % 11 == 0 || i % 13 == 0 || i % 17 == 0)
                primes[i] = false;
        }
        primes[0] = false; primes[1] = false; primes[2] = true;
        primes[2] = true;
        primes[3] = true;
        primes[5] = true;
        primes[7] = true;
        primes[11] = true;
        primes[13] = true;
        primes[17] = true;
        for(int i=18; i<448; i++)
            if(primes[i] == true)
                for(int j=2*i; j<primes.length; j+=i)
                    primes[i] = false;
        */
        System.out.println((1L*(6*n-1)*k));
        for(int i=0; i<n; i++) {
            System.out.println((1L*(6*i+1)*k) + " " + (1L*(6*i+2)*k) + " " + (1L*(6*i+3)*k) + " " + (1L*(6*i+5)*k));
        }
        
                
        // Scanner scan = new Scanner(System.in);
        // PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); 
        // int n = Integer.parseInt(bf.readLine());
        // StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        // int n = Integer.parseInt(st.nextToken());
        // int n = scan.nextInt();
        
        // out.close(); System.exit(0);
    }
}