Vasya and Array

Description:

Input:

The first line contains three integers $$$n, k$$$ and $$$len$$$ ($$$1 \le n \le 10^5, 1 \le k \le 100, 1 \le len \le n$$$).

The second line contains $$$n$$$ numbers — the array. Each number is either $$$-1$$$ or between $$$1$$$ and $$$k$$$ (inclusive).

Output:

Print one integer — the number of ways to replace each $$$-1$$$ with some number from $$$1$$$ to $$$k$$$ (inclusive) so the array is good. The answer may be large, so print it modulo $$$998244353$$$.

Sample Input:

5 2 3
1 -1 1 -1 2

Sample Output:

2

Sample Input:

6 3 2
1 1 -1 -1 -1 -1

Sample Output:

0

Sample Input:

10 42 7
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1

Sample Output:

645711643

Note:

Possible answers in the first test:

1. $$$[1, 2, 1, 1, 2]$$$;
2. $$$[1, 2, 1, 2, 2]$$$.

There is no way to make the array good in the second test, since first two elements are equal.

There are too many answers in the third test, so we won't describe any of them.