Problem Statement

Given is a sequence $a_1,\\dots,a_n$ consisting of $1,\\dots, n$ and $\-1$, along with an integer $d$. How many sequences $p_1,\\dots,p_n$ satisfy the conditions below? Print the count modulo $998244353$.

• $p_1,\\dots,p_n$ is a permutation of $1,\\dots, n$.
• For each $i=1,\\dots,n$, $a_i=p_i$ if $a_i\\neq -1$. (That is, $p_1,\\dots,p_n$ can be obtained by replacing the $\-1$s in $a_1,\\dots,a_n$ in some way.)
• For each $i=1,\\dots,n$, $|p_i - i|\\le d$.

Constraints

• $1 \\le d \\le 5$
• $d < n \\le 500$
• $1\\le a_i \\le n$ or $a_i=-1$.
• $|a_i-i|\\le d$ if $a_i\\neq -1$.
• $a_i\\neq a_j$, if $i\\neq j$ and $a_i, a_j \\neq -1$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$n$ $d$ $a_1$ $\\dots$ $a_n$

Output

Print the number of sequences that satisfy the conditions, modulo $998244353$.

Sample Input 1

4 2
3 -1 1 -1

Sample Output 1

2

The conditions are satisfied by $(3,2,1,4)$ and $(3,4,1,2)$.

Sample Input 2

5 1
2 3 4 5 -1

Sample Output 2

0

The only permutation of $1,2,3,4,5$ that can be obtained by replacing the $\-1$ is $(2,3,4,5,1)$, whose fifth term violates the condition, so the answer is $0$.

Sample Input 3

16 5
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

Sample Output 3

794673086

Print the count modulo $998244353$.