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: from sys import stdin, stdout
  
  N = 998244353
  
  def egcd(a, b):
      """return (g, x, y) such that a*x + b*y = g = gcd(a, b)"""
      if a == 0:
          return (b, 0, 1)
      else:
          g, y, x = egcd(b % a, a)
          return (g, x - (b // a) * y, y)
  
  def modinv(a, m = N):
      """return inverse of a mod m"""
      g, x, y = egcd(a, m)
      if g != 1:
          raise Exception('modular inverse does not exist')
      else:
          return x % m
  
  fact = [1]
  invfact = [1]
  
  for i in range(1,5001):
      fact.append((fact[-1]*i)%N)
      invfact.append((invfact[-1]*modinv(i))%N)
  
  n, k = [int(x) for x in stdin.readline().split()]
  s = stdin.readline().strip()
  
  locations = []
  
  for i in range(n):
      if s[i] == '1':
          locations.append(i)
  
  if k == 0 or len(locations) < k:
      stdout.write('1\n')
  
  else:
      answer = 0
      for i in range(len(locations)-k+1):
          if i == 0:
              lower = 0
          else:
              lower = locations[i-1]+1
  
          if i == len(locations)-k:
              upper = n-1
          else:
              upper = locations[i+k]-1
  
          answer = (answer + fact[upper-lower+1]*invfact[k]*invfact[upper-lower+1-k])%N
  
      for i in range(len(locations)-k):
          lower = locations[i]+1
          upper = locations[i+k]-1
          answer = (answer - fact[upper-lower+1]*invfact[k-1]*invfact[upper-lower+1-k+1])%N
  
      stdout.write(str(answer)+'\n')
  