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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Round272_B {

    public void solve() throws Exception {
    InputReader in = new InputReader();
    int N = in.nextInt();
    int K = in.nextInt();

    StringBuffer ret = new StringBuffer();

    long cur = K;
    for (int i = 0; i < N; i++) {
        ret.append(cur);
        ret.append(' ');

        cur += K;
        ret.append(cur);
        ret.append(' ');

        
        cur += K;
        ret.append(cur);
        ret.append(' ');
        cur += 2 * K;
        ret.append(cur);
        cur += 2 * K;
        ret.append('\n');
    }
    System.out.println(cur-2*K);
    System.out.print(ret);
    }

    public static void main(String[] args) throws Exception {
    new Round272_B().solve();
    }

    static class InputReader {
    BufferedReader in;
    StringTokenizer st;

    public InputReader() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(in.readLine());

    }

    public String next() throws IOException {

        while (!st.hasMoreElements())
        st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(next());
    }
    }
}