# #P1622D. Shuffle

ID: 7567 Type: RemoteJudge 2000ms 512MiB 尝试: 1 已通过: 1 难度: 10 上传者: 标签>combinatoricsmathtwo pointers

# Shuffle

## Description

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\$.

## 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\$.

## Samples

``````7 2
1100110
``````
``````16
``````
``````5 0
10010
``````
``````1
``````
``````8 1
10001000
``````
``````10
``````
``````10 8
0010011000
``````
``````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.