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;
vector<int> ans[4];
int main() {
  cin >> n >> k;
  int i = 1;
  for (int it = 0; it < n; it++) {
    if ((i + 1) % 3 == 0) {
      i++;
      it--;
      continue;
    }
    if (i % 2 == 0) {
      i++;
      it--;
      continue;
    }
    ans[0].push_back(i * k);
    ans[1].push_back((i + 1) * k);
    ans[2].push_back((i + 2) * k);
    ans[3].push_back((i + 4) * k);
    i += 6;
  }
  cout << (i - 2) * k << '\n';
  for (int i = 0; i < (int)ans[0].size(); i++)
    cout << ans[0][i] << ' ' << ans[1][i] << ' ' << ans[2][i] << ' '
         << ans[3][i] << '\n';
  return 0;
}