






from __future__ import annotations




class 							_lowerCAmelCase:





       """simple docstring"""







       def __init__(   self    ,     _lowerCamelCase				):
         UpperCamelCase_:   Union[str, Any]        =							order

         # a_{0} ... a_{k}
         UpperCamelCase_:   Tuple        =							[1.0] + [0.0] * order
         # b_{0} ... b_{k}
         UpperCamelCase_:   List[Any]        =							[1.0] + [0.0] * order

         # x[n-1] ... x[n-k]
         UpperCamelCase_:   Union[str, Any]        =							[0.0] * self.order
         # y[n-1] ... y[n-k]
         UpperCamelCase_:   int        =							[0.0] * self.order





       def      _a       (   self    ,     _lowerCamelCase    ,     _lowerCamelCase				):
         if len(_lowerCamelCase				) < self.order:
           UpperCamelCase_:   Any        =							[1.0, *a_coeffs]

         if len(_lowerCamelCase				) != self.order + 1:
           UpperCamelCase_:   Union[str, Any]        =							(
               f'''Expected a_coeffs to have {self.order + 1} elements '''
               f'''for {self.order}-order filter, got {len(_lowerCamelCase				)}'''
           )
           raise ValueError(_lowerCamelCase				)

         if len(_lowerCamelCase				) != self.order + 1:
           UpperCamelCase_:   int        =							(
               f'''Expected b_coeffs to have {self.order + 1} elements '''
               f'''for {self.order}-order filter, got {len(_lowerCamelCase				)}'''
           )
           raise ValueError(_lowerCamelCase				)

         UpperCamelCase_:   int        =							a_coeffs
         UpperCamelCase_:   Optional[Any]        =							b_coeffs





       def      _a       (   self    ,     _lowerCamelCase				):
         UpperCamelCase_:   List[str]        =							0.0

         # Start at index 1 and do index 0 at the end.
         for i in range(1    ,     self.order + 1				):
           result += (
               self.b_coeffs[i] * self.input_history[i - 1]
               - self.a_coeffs[i] * self.output_history[i - 1]
           )

         UpperCamelCase_:   Any        =							(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

         UpperCamelCase_:   Union[str, Any]        =							self.input_history[:-1]
         UpperCamelCase_:   int        =							self.output_history[:-1]

         UpperCamelCase_:   List[Any]        =							sample
         UpperCamelCase_:   List[str]        =							result

         return result




from bisect import bisect
from itertools import accumulate






def  lowerCamelCase_	(      lowerCAmelCase__	:	int			,	lowerCAmelCase__	:	str			,	lowerCAmelCase__	:	List[str]			,	lowerCAmelCase__	:	List[Any]				)       ->							Union[str, Any]:

							'''simple docstring'''






							A      						=    sorted(zip(lowerCAmelCase__			,	lowerCAmelCase__				)			,	key=lambda lowerCAmelCase__				: x[0] / x[1]			,	reverse=lowerCAmelCase__				)
							A						,   A      						=    [i[0] for i in r], [i[1] for i in r]
							A      						=    list(accumulate(lowerCAmelCase__				)				)
							A      						=    bisect(lowerCAmelCase__			,	lowerCAmelCase__				)
							return (
							    0
							    if k == 0
							    else sum(vl[:k]				) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
							    if k != n
							    else sum(vl[:k]				)
							)


if __name__ == "__main__":
				import doctest

				doctest.testmod()