Problem Statement

Given is a positive integer $M$ and a sequence of $N$ integers: $A = (A_1,A_2,\ldots,A_N)$. Find the number, modulo $998244353$, of sequences of $N+1$ integers, $X = (X_1,X_2, \ldots, X_{N+1})$, satisfying all of the following conditions:

• $1\leq X_i\leq M$ ($1\leq i\leq N+1$)
• $A_iX_i\leq X_{i+1}$ ($1\leq i\leq N$)

Constraints

• $1\leq N\leq 1000$
• $1\leq M\leq 10^{18}$
• $1\leq A_i\leq 10^9$
• $\prod_{i=1}^N A_i \leq M$

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 \ldots A_N

Output

Print the number of integer sequences satisfying the conditions, modulo $998244353$.