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>
class B {
 public:
  int gcd(int a, int b) {
    if (!b) return a;
    return gcd(b, a % b);
  }
  void solve(std::istream& in, std::ostream& out) {
    int n, k;
    in >> n >> k;
    out << (6 * n - 1) * k << "\n";
    int lastCh = 0;
    int lastNech = -1;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < 3; ++j) {
        lastNech += 2;
        out << lastNech * k << " ";
      }
      while (true) {
        lastCh += 2;
        if (lastCh % 3 == 0) continue;
        if (gcd(lastCh, lastNech) != 1 || gcd(lastCh, lastNech - 2) != 1 ||
            gcd(lastCh, lastNech - 4) != 1)
          continue;
        out << lastCh * k << "\n";
        break;
      }
    }
  }
};
int main() {
  B solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}