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 n, k, ans[10005][15], m;
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  scanf("%d%d", &n, &k);
  unordered_map<int, bool> Map;
  m = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= 4; j++) {
      ans[i][j] = 6 * (i - 1) + j;
      if (j == 4) ans[i][j]++;
      ans[i][j] *= k;
      m = max(m, ans[i][j]);
    }
  }
  printf("%d\n", m);
  for (int i = 1; i <= n; i++)
    printf("%d %d %d %d\n", ans[i][1], ans[i][2], ans[i][3], ans[i][4]);
  return 0;
}