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.