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>
const int MOD = 1000000007;
const int INF = 0x3F3F3F3F;
const double EPS = 1e-6;
const int MaxN = 400005;
const int P[] = {1, 2, 3, 5};
int main() {
  int N, K;
  while (scanf("%d%d", &N, &K) == 2) {
    printf("%d\n", K * (6 * N - 1));
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < 4; j++) {
        printf("%d%c", (6 * i + P[j]) * K, j == 3 ? '\n' : ' ');
      }
    }
  }
  return 0;
}