Sum Over All Arrays

Consider an array $B$ of length $M$. The *beauty* of $B$ is defined as $\sum_{i=1}^{M} |B_i-B_{M+1-i}|$. The **score** of $B$ is the **maximum** *beauty* over **all** permutations of $B$. You are given positive integers $N$ and $X$. Find the sum of **scores** of all arrays $A$ of length $N$, such that $1 \leq A_i \leq X$. Since the sum might be large, please print it modulo $998244353$.