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.

• 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.
• 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.

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

见题面 Input 部分

见题面 Output 部分