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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k, a1, a2, a3, a4, b1, b2;
  int impar = 1;
  int par = 2;
  cin >> n >> k;
  cout << k * (6 * n - 1) << "\n";
  for (int i = 0; i < n; ++i) {
    a1 = k * impar;
    impar += 2;
    a2 = k * impar;
    impar += 2;
    a3 = k * impar;
    impar += 2;
    b1 = a1 / k + 1;
    b2 = a2 / k + 1;
    if ((a3 / k - b1) % 3 == 0)
      a4 = k * b2;
    else
      a4 = k * b1;
    cout << a1 << " " << a2 << " " << a3 << " " << a4 << "\n";
  }
}