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 $D_i$.

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.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $D_1$ $\\ldots$ $D_N$

Output

Print the answer.

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 $998244353$.