### Problem Statement

We have a sequence of length $N$ consisting of integers between $0$ and $M$, inclusive: $A=(A_1,A_2,\dots,A_N)$.

Snuke will perform the following operations 1 and 2 in order.

1.  For each $i$ such that $A_i=0$, independently choose a uniform random integer between $1$ and $M$, inclusive, and replace $A_i$ with that integer.
2.  Sort $A$ in ascending order.

Print the expected value of $A_K$ after the two operations, modulo $998244353$.

How to print a number modulo $998244353$? It can be proved that the sought expected value is always rational. Additionally, under the Constraints of this problem, when that value is represented as $\frac{P}{Q}$ using two coprime integers $P$ and $Q$, it can be proved that there is a unique integer $R$ such that $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R \lt 998244353$. Print this $R$.

### Input

The input is given from Standard Input in the following format:

```
$N$ $M$ $K$
$A_1$ $A_2$ $\dots$ $A_N$
```

### Output

Print the expected value of $A_K$ after the two operations, modulo $998244353$.

### Constraints

-   $1\leq K \leq N \leq 2000$
-   $1\leq M \leq 2000$
-   $0\leq A_i \leq M$
-   All values in the input are integers.

3

In the operation 1, Snuke will replace $A_2$ with an integer between 1 and 5. Let x be this integer.

• If x=1 or 2, we will have $A_2=2$ after the two operations.
• If x=3, we will have $A_2=3$ after the two operations.
• If x=4 or 5, we will have $A_2=4$ after the two operations.

Thus, the expected value of $A_2$ is $\frac{2+2+3+4+4}{5}=3$.

221832080

The expected value is $\frac{14}{9}$.