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.*;
import java.math.*;


public class Main {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
    
    
    static void solve() throws Exception {
        int n = nextInt();
        int k = nextInt();
        int[][] ans = new int[n][4];
        Queue<Integer> q = new LinkedList<Integer>();
        int maxV = 0;
        int cur = 3;
        for (int i = 0; i < n; ++i) {
            ans[i][1] = cur - 2;
            ans[i][2] = cur;
            ans[i][3] = cur + 2;
            q.add(cur - 1);
            q.add(cur + 1);
            q.add(cur + 3);
            maxV = Math.max(cur + 2, maxV);
            cur += 6;
            while (true) {
                int x = q.poll();
                if (gcd(ans[i][1], x) == 1 && gcd(ans[i][2], x) == 1 && gcd(ans[i][3], x) == 1) {
                    ans[i][0] = x;
                    maxV = Math.max(x, maxV);
                    break;
                }
            }
        }
        out.println(maxV * k);
        for (int i = 0; i < n; ++i) {
            out.println((ans[i][0] * k) + " " + (ans[i][1] * k) + " " + (ans[i][2] * k) + " " + (ans[i][3] * k));
        }
    }
    
    static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }
    
    static long sqr(int x) {
        return (long)x * x;
    }
    
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }
    
    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    static String nextLine() throws IOException {
        tok = new StringTokenizer("");
        return in.readLine();
    }

    static boolean hasNext() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return false;
            }
            tok = new StringTokenizer(s);
        }
        return true;
    }

    public static void main(String args[]) {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //in = new BufferedReader(new FileReader("input.in"));
            //out = new PrintWriter(new FileWriter("output.out"));
            solve();
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            java.lang.System.exit(1);
        }
    }
}