Shuffle

Description:

Input:

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.

Output:

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 $$$998244353$$$.

Sample Input:

7 2
1100110

Sample Output:

16

Sample Input:

5 0
10010

Sample Output:

1

Sample Input:

8 1
10001000

Sample Output:

10

Sample Input:

10 8
0010011000

Sample Output:

1

Note:

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.