Takahashi is participating in a lottery.

Each time he takes a draw, he gets one of the $N$ prizes available. Prize $i$ is awarded with probability $\frac{W_i}{\sum_{j=1}^{N}W_j}$. The results of the draws are independent of each other.

What is the probability that he gets exactly $M$ different prizes from $K$ draws? Find it modulo $998244353$.

Note

To print a rational number, start by representing it as a fraction $\frac{y}{x}$. Here, $x$ and $y$ should be integers, and $x$ should not be divisible by $998244353$ (under the Constraints of this problem, such a representation is always possible). Then, print the only integer $z$ between $0$ and $998244352$ (inclusive) such that $xz\equiv y \pmod{998244353}$.

Input is given from Standard Input in the following format:

```
$N$ $M$ $K$
$W_1$
$\vdots$
$W_N$
```

Print the answer.

-   $1 \leq K \leq 50$
-   $1 \leq M \leq N \leq 50$
-   $0 < W_i$
-   $0 < W_1 + \ldots + W_N < 998244353$
-   All values in input are integers.

221832079

Each draw awards Prize 1 with probability $\frac{2}{3}$ and Prize 2 with probability $\frac{1}{3}$.

He gets Prize 1 at both of the two draws with probability $\frac{4}{9}$, and Prize 2 at both draws with probability $\frac{1}{9}$, so the sought probability is $\frac{5}{9}$.

The modulo 998244353 representation of this value, according to Note, is 221832079221832079.

0

It is impossible to get three different prizes from two draws, so the sought probability is 0.