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.
  
  Input
  
  The first line contains two integers n and k (2 ≤ n ≤ 5000; 0 ≤ k ≤ 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.
  
  Examples
  
  Input
  
  
  7 2
  1100110
  
  
  Output
  
  
  16
  
  
  Input
  
  
  5 0
  10010
  
  
  Output
  
  
  1
  
  
  Input
  
  
  8 1
  10001000
  
  
  Output
  
  
  10
  
  
  Input
  
  
  10 8
  0010011000
  
  
  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.
solution: import java.io.*;
  import java.util.*;
  
  public class d {
      public static void main(String[] args) throws Exception {
          BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
          PrintWriter out = new PrintWriter(System.out);
          StringTokenizer tokenizer = new StringTokenizer(in.readLine());
          int n = Integer.parseInt(tokenizer.nextToken());
          int k = Integer.parseInt(tokenizer.nextToken());
          int mod = 998244353;
          boolean[] input = new boolean[n];
          String s = in.readLine();
          int[] prefix = new int[n];
          int[][] ncr = new int[n + 1][n + 1];
          ncr[0][0] = 1;
          for (int i = 0; i < n; i++) {
              for (int j = 0; j <= i; j++) {
                  ncr[i + 1][j] += ncr[i][j];
                  ncr[i + 1][j] %= mod;
                  ncr[i + 1][j + 1] += ncr[i][j];
                  ncr[i + 1][j + 1] %= mod;
              }
          }
          for (int i = 0; i < ncr.length; i++) {
              // System.out.println(Arrays.toString(ncr[i]));
          }
          for (int i = 0; i < n; i++) {
              if (s.charAt(i) == '1')
                  input[i] = true;
              prefix[i] = input[i] ? 1 : 0;
              if (i > 0)
                  prefix[i] += prefix[i - 1];
          }
          int answer = 1;
          if (prefix[n - 1] >= k) {
              for (int i = 0; i < n; i++) {
                  int pre = i > 0 ? prefix[i - 1] : 0;
                  for (int j = i + 1; j < n; j++) {
                      if (prefix[j] > pre + k)
                          continue;
                      int cnt1 = prefix[j] - pre;
                      int cnt0 = j - i + 1 - cnt1;
                      if (input[i]) {
                          cnt0--;
                      } else {
                          cnt1--;
                      }
                      if (input[j]) {
                          cnt0--;
                      } else {
                          cnt1--;
                      }
                      if (cnt0 < 0 || cnt1 < 0)
                          continue;
                      answer += ncr[cnt1 + cnt0][cnt0];
                      answer %= mod;
                  }
              }
  
          }
  
          System.out.println(answer);
          in.close();
          out.close();
      }
  }