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:
k,n=map(int,raw_input().split())
print n*(6*k-1)
cnt=1
def gcd(a,b):return a if not b else gcd(b, a%b)
def getNext(cnt, x, y, z):
    while gcd(cnt,x) != 1 or gcd(cnt,y) != 1 or  gcd(cnt,z) != 1: cnt+=2
    return cnt>>1
for i in range(1,k+1): 
    print cnt*n*2, n*(6*i-5),n*(6*i-3),n*(6*i-1)
    cnt+=1
    if cnt%3==0: cnt+=1
    cnt = getNext(cnt*2, (6*i+1),(6*i+3),(6*i+5))