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 PYTHON):

Solution:
import sys
from collections import defaultdict

n, k = map(int, sys.stdin.readline().strip().split())

used = defaultdict(lambda: False)
print k*(6*n-1)

def gcd(a, b):
  if a < b:
    return gcd(b, a)
  elif b == 0:
    return a
  else:
    return gcd(b, a%b)

def ok(lst, e):
  for l in lst:
    if gcd(l, e) != 1:
      return False
  return True

for i in range(n):
  a = 6*i+1
  b = 6*i+3
  c = 6*i+5
  print k*a, k*b, k*c, 
  lst = [a,b,c]

  cnt = 0
  while True:
    e = 6*i+4-2*cnt
    if not used[e] and ok(lst,e):
      used[e] = True
      print k*e
      break
    else:
      cnt += 1