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
  
  
  def solve():
      MOD = 998244353
      inp = sys.stdin.readline
      n, k = map(int, inp().split())
      s = list(map(int, inp().strip()))
      if sum(s) < k:
          print(1)
          return
      C = [None] * n
      C[0] = [1]
      for i in range(1,n):
          a = [None] * (i + 1)
          C[i] = a
          b = C[i-1]
          a[0] = 1
          a[i] = 1
          for j in range(1, i):
              a[j] = (b[j - 1] + b[j]) % MOD
      r = 1
      for i in range(n):
          #a = s[i]
          #for j in range(i + 1, n):
          #    a += s[j]
          #if True:#a >= k:
              c = [0, 0]
              a = s[i]
              c[a] += 1
              for j in range(i + 1, n):
                  b = s[j]
                  c[b] += 1
                  if c[1] > k:
                      break
                  if c[b^1] > 0:
                     c[b^1] -= 1
                     if c[a^1] > 0:
                        c[a^1] -= 1
                        #print(i, j, C[j - i - 1][c[0]])
                        #if j - i - 1 != sum(c):
                        #    print('wut', j - i - 1, c)
                        r = (r + C[j - i - 1][c[0]]) % MOD
                        c[a^1] += 1
                     c[b^1] += 1
      print(r)
  
  
  def main():
      #for i in range(int(sys.stdin.readline())):
      solve()
  
  if __name__ == '__main__':
      main()
  