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;
struct node {
  int A, B, C, D;
  node(int _A = 0, int _B = 0, int _C = 0, int _D = 0) {
    A = _A;
    B = _B;
    C = _C;
    D = _D;
  }
};
vector<node> ans;
int n, k;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++)
    ans.push_back(node((i - 1) * 6 + 1, (i - 1) * 6 + 2, (i - 1) * 6 + 3,
                       (i - 1) * 6 + 5));
  int maxv = 0;
  for (int i = 0; i < ans.size(); i++) {
    ans[i].A *= k;
    ans[i].B *= k;
    ans[i].C *= k;
    ans[i].D *= k;
    maxv = max(maxv, ans[i].A);
    maxv = max(maxv, ans[i].B);
    maxv = max(maxv, ans[i].C);
    maxv = max(maxv, ans[i].D);
  }
  printf("%d\n", maxv);
  for (int i = 0; i < ans.size(); i++)
    printf("%d %d %d %d\n", ans[i].A, ans[i].B, ans[i].C, ans[i].D);
  return 0;
}