CF1477F.Nezzar and Chocolate Bars

Nezzar buys his favorite snack — $n$ chocolate bars with lengths $l_1,l_2,\ldots,l_n$. However, chocolate bars might be too long to store them properly!

In order to solve this problem, Nezzar designs an interesting process to divide them into small pieces. Firstly, Nezzar puts all his chocolate bars into a black box. Then, he will perform the following operation repeatedly until the maximum length over all chocolate bars does not exceed $k$.

• Nezzar picks a chocolate bar from the box with probability proportional to its length $x$.
• After step $1$, Nezzar uniformly picks a real number $r \in (0,x)$ and divides the chosen chocolate bar into two chocolate bars with lengths $r$ and $x-r$.
• Lastly, he puts those two new chocolate bars into the black box.

Nezzar now wonders, what is the expected number of operations he will perform to divide his chocolate bars into small pieces.

It can be shown that the answer can be represented as $\frac{P}{Q}$, where $P$ and $Q$ are coprime integers and $Q \not \equiv 0$ ($\bmod 998\,244\,353$). Print the value of $P\cdot Q^{-1} \mod 998\,244\,353$.

Nezzar 购买了他最喜爱的零食——$n$ 块长度分别为 $l_1, l_2, \ldots, l_n$ 的巧克力棒。然而，这些巧克力棒可能过长，难以妥善存放！

为了解决这个问题，Nezzar 设计了一种有趣的分割过程，将它们切分为更小的段。首先，Nezzar 将所有巧克力棒放入一个黑箱中。然后，他将重复执行以下操作，直到所有巧克力棒中的最大长度不超过 $k$。

• Nezzar 以与巧克力棒当前长度 $x$ 成正比的概率，从黑箱中随机选取一根巧克力棒；
• 在第 1 步之后，Nezzar 在区间 $(0, x)$ 内均匀随机选取一个实数 $r$，并将所选巧克力棒切成两段，长度分别为 $r$ 和 $x - r$；
• 最后，他将这两段新巧克力棒放回黑箱中。

Nezzar 现在想知道：他需要执行的操作次数的期望值是多少？

可以证明，该答案可表示为 $\frac{P}{Q}$，其中 $P$ 与 $Q$ 互质，且 $Q \not\equiv 0 \pmod{998\,244\,353}$。请输出 $P \cdot Q^{-1} \bmod 998\,244\,353$ 的值。

The first line contains two integers $n$ and $k$ ($1 \le n \le 50, 1 \le k \le 2000$).

The second line contains $n$ integers $l_1, l_2, \ldots, l_n$ ($1 \le l_i$, $\sum_{i=1}^{n} l_i \le 2000$).

第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 50$，$1 \le k \le 2000$）。

第二行包含 $n$ 个整数 $l_1, l_2, \ldots, l_n$（$1 \le l_i$，且 $\sum_{i=1}^{n} l_i \le 2000$）。

Print a single integer — the expected number of operations Nezzar will perform to divide his chocolate bars into small pieces modulo $998\,244\,353$.

输出一个整数——Nezzar 将巧克力棒分割成小块所需的期望操作次数，对 $998\,244\,353$ 取模。