output_description: Find the number of strings, modulo 998244353, that can result from applying
  the operation on S between 0 and K times (inclusive).
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      S K
attempt: s, k = map(int, input().split())
  
problem_description: Statement
  
  Given is a string S consisting of `0` and `1`. Find the number of strings,
  modulo 998244353, that can result from applying the following operation on S
  between 0 and K times (inclusive):
  
    * Choose a pair of integers i, j (1\leq i < j\leq |S|) such that the i-th and j-th characters of S are `0` and `1`, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.
samples: [{"input": "0101 1", "output": "4\n    \n\nFour strings, `0101`, `0110`, `1001`, and `1010`, can result.\n\n* * *"}, {"input": "01100110 2", "output": "14\n    \n\n* * *"}, {"input": "1101010010101101110111100011011111011000111101110101010010101010101 20", "output": "113434815"}]