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
  
  n, k = map(int, input().split())
  mod = 998244353
  s = list(input().rstrip())
  l = n + 5
  fact = [1] * (l + 1)
  for i in range(1, l + 1):
      fact[i] = i * fact[i - 1] % mod
  inv = [1] * (l + 1)
  inv[l] = pow(fact[l], mod - 2, mod)
  for i in range(l - 1, -1, -1):
      inv[i] = (i + 1) * inv[i + 1] % mod
  
  def comb(n, r):
      return fact[n] * inv[r] % mod * inv[n - r] % mod if n >= r >= 0 else 0
  
  x = [-1]
  for i in range(n):
      if s[i] == "1":
          x.append(i)
  x.append(n)
  l = len(x) - 1
  ans = 1
  for i in range(1, len(x) - 1):
      xi = x[i]
      l = i - 1 if i < k else x[i - k] + 1
      for j in range(l, x[i + 1]):
          if xi == j:
              continue
          c = min(i - 1, k - 1)
          m = j - 1 - x[max(0, i - k)]
          ans += comb(m, c)
          ans %= mod
  if len(x) - 2 < k:
      ans = 1
  print(ans)