D. Shuffletime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint 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.ExamplesInput
7 2
1100110
Output
16
Input
5 0
10010
Output
1
Input
8 1
10001000
Output
10
Input
10 8
0010011000
Output
1
NoteSome 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.
7 2
1100110

16 
['combinatorics', 'math', 'two pointers', '*2000']