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:
from fractions import gcd

def get_last(my_list):
	i = my_list[-1] + 1
	while True:
		good_i = True
		for j in my_list:
			if gcd(i, j) != 1:
				good_i = False
				break
		if good_i:
			return i
		i += 1

def main():
	n, k = map(int, raw_input().split())
	lists = []
	lists.append([1, 2, 3, 5])
	for m_set in xrange(n - 1):
		#first = get_last(lists[-1])
		first = lists[-1][-1] + 2
		curr_list = []
		curr_list.append(first)
		for i in xrange(3):
			curr_list.append(get_last(curr_list))
		lists.append(curr_list)
	print lists[-1][-1] * k
	for l in lists:
		for i, num in enumerate(l):
			print l[i] * k,
		print

main()