
'''simple docstring'''
def        A_     (						__SCREAMING_SNAKE_CASE						:  int = 3			,     __SCREAMING_SNAKE_CASE						:  int = 7			,     __SCREAMING_SNAKE_CASE						:  int = 100_0000 )				->       int:





  """simple docstring"""

  __A		:     Optional[Any]												=		0
  __A		:     int												=		1

  for current_denominator in range(1			,     limit + 1 ):
    __A		:     Dict												=		current_denominator * numerator // denominator
    if current_denominator % denominator == 0:
      current_numerator -= 1
    if current_numerator * max_denominator > current_denominator * max_numerator:
      __A		:     Optional[int]												=		current_numerator
      __A		:     str												=		current_denominator
  return max_numerator


if __name__ == "__main__":
     print(solution(numerator=3, denominator=7, limit=1_000_000))





'''simple docstring'''
def        A_     (						__SCREAMING_SNAKE_CASE						:  list			,     __SCREAMING_SNAKE_CASE						:  list			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int )				->       int:





  """simple docstring"""

  if index == number_of_items:
    return 0
  __A		:     List[Any]												=		0
  __A		:     Union[str, Any]												=		0
  __A		:     List[Any]												=		knapsack(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     index + 1 )
  if weights[index] <= max_weight:
    __A		:     Tuple												=		values[index] + knapsack(
        __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     max_weight - weights[index]			,     index + 1 )
  return max(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
     import doctest

     doctest.testmod()



