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 $998244353$.