A14840. Shuffle

You are given a binary string (i. e. a string consisting of characters 0 and/or 1) $s$ of length $n$ . You can perform the following operation with the string $s$ at most once: choose a substring (a contiguous subsequence) of $s$ having exactly $k$ characters 1 in it, and shuffle it (reorder the characters in the substring as you wish).

Calculate the number of different strings which can be obtained from $s$ by performing this operation at most once.

The first line contains two integers $n$ and $k$ ( $2 \le n \le 5000$ ; $0 \le k \le n$ ).

The second line contains the string $s$ of length $n$ , consisting of characters 0 and/or 1.

Print one integer — the number of different strings which can be obtained from $s$ by performing the described operation at most once. Since the answer can be large, output it modulo $998244353$ .

Some strings you can obtain in the first example:

- to obtain 0110110, you can take the substring from the $1$ -st character to the $4$ -th character, which is 1100, and reorder its characters to get 0110;
- to obtain 1111000, you can take the substring from the $3$ -rd character to the $7$ -th character, which is 00110, and reorder its characters to get 11000;
- to obtain 1100101, you can take the substring from the $5$ -th character to the $7$ -th character, which is 110, and reorder its characters to get 101.

In the second example, $k = 0$ so you can only choose the substrings consisting only of 0 characters. Reordering them doesn't change the string at all, so the only string you can obtain is 10010.