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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Temp {
	class FastSolver {

		public void Solve() {
			int n = ni();
			int k = ni();
			int pos = 1;
			System.out.println(k*(6*n-1));
			for (int i = 1; i <= n; i++) {
				while (pos % 3 == 0)
					pos++;
				if (pos % 2 == 0) {
					System.out.println(k*pos + " " + k*(pos + 1) + " " + k*(pos + 3)
							+ " " + k*(pos + 4));
				} else {
					System.out.println(k*pos + " " + k*(pos + 1) + " " + k*(pos + 2)
							+ " " + k*(pos + 4));
				}
				pos += 5;
			}

		}

		BufferedReader br;
		StringTokenizer st;

		public FastSolver(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String n() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		String l() {
			String s = null;
			try {
				s = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return s;

		}

		boolean hasMoreTokens() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

		int nb() {
			return Integer.parseInt(n(), 2);
		}

		long nbl() {
			return Long.parseLong(n(), 2);
		}

		int ni() {
			return Integer.parseInt(n());
		}

		double nd() {
			return Double.parseDouble(n());
		}

		long nl() {
			return Long.parseLong(n());
		}
	}

	public void run() {
		FastSolver in = new FastSolver(System.in);
		PrintWriter out = new PrintWriter(System.out);
		in.Solve();
		out.close();
	}

	public static void main(String[] args) {
		new Temp().run();
	}
}