Problem Statement

We have N bags.
Bag i contains L_i balls. The $j-th ball (1\leq j\leq L_i)$ in Bag i has a positive integer a_{i,j} written on it.
We will pick out one ball from each bag.
How many ways are there to pick the balls so that the product of the numbers written on the picked balls is X?
Here, we distinguish all balls, even with the same numbers written on them.

Input

Input is given from Standard Input in the following format:
N X
$L_1 a_{1,1} a_{1,2} \ldots a_{1,L_1}$
$L_2 a_{2,1} a_{2,2} \ldots a_{2,L_2}$
$\vdots$
$L_N a_{N,1} a_{N,2} \ldots a_{N,L_N}$

Output

Print the answer.

Constraints

• $N \geq 2$
• $L_i \geq 2$
• The product of the numbers of balls in the bags is at most 10^5: $\displaystyle\prod_{i=1}^{N}L_i \leq 10^5$.
• $1 \leq a_{i,j} \leq 10^9$
• $1 \leq X \leq 10^{18}$
• All values in input are integers.

Sample Input 1

2 40
3 1 8 4
2 10 5

Sample Output 1

2

When choosing the 3-rd ball in Bag 1 and 1-st ball in Bag 2, we have $a_{1,3} \times a_{2,1} = 4 \times 10 = 40$.
When choosing the 2-nd ball in Bag 1 and 2-nd ball in Bag 2, we have $a_{1,2} \times a_{2,2} = 8 \times 5 = 40$.
There are no other ways to make the product 40, so the answer is 2.

Sample Input 2

3 200
3 10 10 10
3 10 10 10
5 2 2 2 2 2

Sample Output 2

45

Note that we distinguish all balls, even with the same numbers written on them.

Sample Input 3

3 1000000000000000000
2 1000000000 1000000000
2 1000000000 1000000000
2 1000000000 1000000000

Sample Output 3

0

There may be no way to make the product X.

见题面 Input 部分

见题面 Output 部分