






'''simple docstring'''





def    lowerCamelCase_     (    lowercase__ = 1000):
	return sum(e for e in range(3				,     lowercase__) if e % 3 == 0 or e % 5 == 0)


if __name__ == "__main__":
	print(F"""{solution() = }""")









'''simple docstring'''





from __future__ import annotations
class 				lowercase       :


    '''simple docstring'''

    def __init__(					self     :     Optional[int]				,     __lowerCamelCase     :     int     )							->							None:

     '''simple docstring'''




     lowerCamelCase__  =     order

     # a_{0} ... a_{k}
     lowerCamelCase__  =     [1.0] + [0.0] * order
     # b_{0} ... b_{k}
     lowerCamelCase__  =     [1.0] + [0.0] * order

     # x[n-1] ... x[n-k]
     lowerCamelCase__  =     [0.0] * self.order
     # y[n-1] ... y[n-k]
     lowerCamelCase__  =     [0.0] * self.order

    def    a__				(					self     :     Dict				,     __lowerCamelCase     :     list[float]				,     __lowerCamelCase     :     list[float]     )							->							None:

     '''simple docstring'''




     if len(__lowerCamelCase     ) < self.order:
      lowerCamelCase__  =     [1.0, *a_coeffs]

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

     lowerCamelCase__  =     a_coeffs
     lowerCamelCase__  =     b_coeffs




    def    a__				(					self     :     Dict				,     __lowerCamelCase     :     float     )							->							float:

     '''simple docstring'''




     lowerCamelCase__  =     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]
      )

     lowerCamelCase__  =     (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

     lowerCamelCase__  =     self.input_history[:-1]
     lowerCamelCase__  =     self.output_history[:-1]

     lowerCamelCase__  =     sample
     lowerCamelCase__  =     result

     return result

