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: def main():
      n, k = map(int, raw_input().split())
      s = raw_input().strip()
      b = [0] * (n + 1)
      a = []
      for i, x in enumerate(s):
          b[i+1] = b[i]
          if x == '1':
              a.append(i)
              b[i+1] += 1
      a.append(n)
      if b[-1] < k:
          print 1
          return
      mod = 998244353
      f = [1] * (n + 1)
      for i in xrange(2, n + 1):
          f[i] = f[i-1] * i % mod
      invf = [1] * (n + 1)
      invf[-1] = pow(f[-1], mod - 2, mod)
      for i in xrange(n, 1, -1):
          invf[i-1] = invf[i] * i % mod
      def C(N, K):
          if K < 0 or K > N:
              return 0
          return f[N] * invf[K] * invf[N-K] % mod
      ans = 1
      l = len(a)
      for i, x in enumerate(s):
          j = b[i] + k
          if j >= l:
              j = l - 1
          c = j - b[i]
          r = a[j] - i
          if x == '1':
              ans += C(r - 1, c)
              if ans >= mod:
                  ans -= mod
          else:
              ans += C(r - 1, c - 1)
              if ans >= mod:
                  ans -= mod
      print ans
  
  main()
  