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 PYTHON3):

Solution:
#!/usr/bin/python3

import sys
import heapq

def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

def compatible(n, s):
    for m in s:
        if gcd(n, m) > 1:
            return False
    return True

if __name__ == '__main__':
    n, k = map(int, sys.stdin.readline().split())
    
    print(((n-1)*6 + 5) * k)
    for i in range(n):
        s = [6*i + 1, 6*i + 2, 6*i + 3, 6*i + 5]
        print(' '.join(str(k*i) for i in s))