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 $$$998244353$$$.
7 2 1100110
16
5 0 10010
1
8 1 10001000
10
10 8 0010011000
1
Some strings you can obtain in the first example:
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.
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