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 sys
  input = sys.stdin.readline
  mod = 998244353
  
  
  def power(num, ex):
      pw, res = num, 1
      while ex:
          if ex & 1:
              res = res * pw
          pw = pw * pw
          ex >>= 1
      return res
  
  
  def power_with_modulo(num, ex):
      pw, res = num % mod, 1
      while ex:
          if ex & 1:
              res = res * pw % mod
          pw = pw * pw % mod
          ex >>= 1
      return res
  
  
  n, k = map(int, input().split())
  s = str(input())
  ans = 1
  prefix_sum = [0 for i in range(n)]
  fac = [1 for i in range(n+1)]
  
  
  for i in range(1, n+1):
      fac[i] = (fac[i-1]*i) % mod
  
  prefix_sum[0] = 1 if s[0] == '1' else 0
  for i in range(1, n):
      prefix_sum[i] = prefix_sum[i-1] + int(s[i] == '1')
  
  if prefix_sum[n-1] < k:
      print(1)
      exit()
  
  C = [[0 for i in range(n+1)] for i in range(n+1)]
  C[0][0] = 1
  for i in range(1, n+1):
      C[i][0] = 1
      for j in range(1, i+1):
          C[i][j] = (C[i-1][j] + C[i-1][j-1]) % mod
  
  #print(C)
  for i in range(n):
      for j in range(i+1, n):
          cnt = (j-i+1)
          cnt1 = prefix_sum[j] - (prefix_sum[i-1] if i >= 1 else 0)
          if cnt1 > k:
              continue
          cnt -= 2
          if s[i] == '0':
              cnt1 -= 1
          if s[j] == '0':
              cnt1 -= 1
          if (cnt1 >= 0) and (cnt >= cnt1):
              ans = (ans+C[cnt][cnt1]) % mod
  
  print(ans)
  
  
  
  
  
  