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 x[10005][4];
vector<int> ans;
int main(void) {
  int a, b;
  scanf("%d %d", &a, &b);
  x[0][0] = 1;
  x[0][1] = 2;
  x[0][2] = 3;
  x[0][3] = 5;
  int i = 0;
  do {
    for (int j = 0; j < 4; j++) {
      ans.push_back(x[i][j] * b);
      x[i + 1][j] = x[i][j] + 6;
    }
    i++;
  } while (i < a);
  printf("%d\n", ans.back());
  for (int i = 0; i < ans.size(); i++) {
    printf("%d ", ans[i]);
    if (!((i + 1) % 4)) puts("");
  }
}