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 $R$.

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.

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 $998244353$.

Sample Input 1

3 5 2
2 0 4

Sample Output 1

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 $\\frac{2+2+3+4+4}{5}=3$.

Sample Input 2

2 3 1
0 0

Sample Output 2

221832080

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

Sample Input 3

10 20 7
6 5 0 2 0 0 0 15 0 0

Sample Output 3

617586310