F. Vasya and Array
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Vasya has got an array consisting of $n$ integers, and two integers $k$ and $len$ in addition. All numbers in the array are either between $1$ and $k$ (inclusive), or equal to $-1$. The array is good if there is no segment of $len$ consecutive equal numbers.

Vasya will replace each $-1$ with some number from $1$ to $k$ (inclusive) in such a way that the resulting array is good. Tell him the number of ways to do this replacement. Since the answer may be large, print it modulo $998244353$.

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 $998244353$.

Examples
Input
5 2 3
1 -1 1 -1 2

Output
2

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

Output
0

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

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.