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;
map<int, int> mp;
int maxx = -1;
void start() {
  cin >> n >> k;
  int prev = 0;
  int start = 0;
  int times = 0;
  vector<int> s[n];
  while (times < n) {
    if (times == n - 1) {
      s[times].push_back(start + k);
      s[times].push_back(start + 3 * k);
      s[times].push_back(start + 4 * k);
      s[times].push_back(start + 5 * k);
      times++;
    } else {
      s[times].push_back(start + k);
      s[times].push_back(start + 3 * k);
      s[times].push_back(start + 4 * k);
      s[times].push_back(start + 5 * k);
      times++;
      start = start + 6 * k;
    }
  }
  cout << s[n - 1].back() << '\n';
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < s[i].size(); j++) {
      if (j != 0) cout << " ";
      cout << s[i][j];
    }
    cout << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  start();
  return 0;
}