Problem Statement

Given are positive integers N, M, and a sequence of positive integers $D = (D_1, \dots, D_N)$.
Find the number of sequences of positive integers $A = (A_1, \dots, A_N)$ that satisfy the following conditions, modulo 998244353.

• $1 \leq A_i \leq M$ $, (1 \leq i \leq N)$
• $A_i \neq A_j$ $, (1 \leq i \lt j \leq N)$
• For each i $, (1 \leq i \leq N), A_i$ is a multiple of D_i.

Input

Input is given from Standard Input in the following format:
N M
$D_1 \ldots D_N$

Output

Print the answer.

Constraints

• $2 \leq N \leq 16$
• $1 \leq M \leq 10^{18}$
• $1 \leq D_i \leq M$ $, (1 \leq i \leq N)$
• All values in input are integers.

Sample Input 1

3 7
2 3 4

Sample Output 1

3

The three sequences A that satisfy the conditions are (2, 3, 4), (2, 6, 4), (6, 3, 4).

Sample Input 2

3 3
1 2 2

Sample Output 2

0

No sequence A satisfies the conditions.

Sample Input 3

6 1000000000000000000
380214083 420492929 929717250 666796775 209977152 770361643

Sample Output 3

325683519

Be sure to find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分