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;
struct pack {
  int a, b, c, d;
  pack(int _a, int _b, int _c, int _d) {
    a = _a;
    b = _b;
    c = _c;
    d = _d;
  }
  pack() {}
};
vector<pack> res;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, k;
  cin >> n >> k;
  int m = 0;
  int odd = 1;
  int even = 2;
  for (int i = 1; i <= n; i++) {
    int x, d[3];
    x = even * k;
    even += 2;
    if (even % 3 == 0) even += 2;
    for (int j = 0; j <= 2; j++) {
      d[j] = odd * k;
      odd += 2;
      m = max(m, d[j]);
    }
    m = max(m, x);
    res.push_back(pack(x, d[0], d[1], d[2]));
  }
  cout << m << "\n";
  for (__typeof(res.begin()) it = res.begin(); it != res.end(); it++) {
    pack t = *it;
    cout << t.a << " " << t.b << " " << t.c << " " << t.d << "\n";
  }
  return 0;
}