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:
class CodeforcesTask477BSolution:
    def __init__(self):
        self.result = ''
        self.n_k = []

    def read_input(self):
        self.n_k = [int(x) for x in input().split(" ")]

    def process_task(self):
        m = (6 * self.n_k[0] - 1) * self.n_k[1]
        results = []
        for x in range(self.n_k[0]):
            results.append([6 * x + 1, 6 * x + 2, 6 * x + 3, 6 * x + 5])
        self.result = "{0}\n{1}".format(m, "\n".join([" ".join([str(x * self.n_k[1]) for x in res]) for res in results]))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask477BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())