





"""simple docstring"""





from math import isclose, sqrt


def 			UpperCAmelCase__							(  SCREAMING_SNAKE_CASE     :						float							,						SCREAMING_SNAKE_CASE     :						float							,						SCREAMING_SNAKE_CASE     :						float			):







      '''simple docstring'''




      lowerCAmelCase  						=       point_y / 4 / point_x
      lowerCAmelCase  						=       2 * normal_gradient / (1 + normal_gradient * normal_gradient)
      lowerCAmelCase  						=       (1 - normal_gradient * normal_gradient) / (
          1 + normal_gradient * normal_gradient
      )
      lowerCAmelCase  						=       (sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

      # to find the next point, solve the simultaeneous equations:
      # y^2 + 4x^2 = 100
      # y - b = m * (x - a)
      # ==> A x^2 + B x + C = 0
      lowerCAmelCase  						=       outgoing_gradient**2 + 4
      lowerCAmelCase  						=       2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
      lowerCAmelCase  						=       (point_y - outgoing_gradient * point_x) ** 2 - 1_00

      lowerCAmelCase  						=       (
          -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term			)
      ) / (2 * quadratic_term)
      lowerCAmelCase  						=       (
          -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term			)
      ) / (2 * quadratic_term)

      # two solutions, one of which is our input point
      lowerCAmelCase  						=       x_minus if isclose(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE			) else x_plus
      lowerCAmelCase  						=       point_y + outgoing_gradient * (next_x - point_x)

      return next_x, next_y, outgoing_gradient


def 			UpperCAmelCase__							(  SCREAMING_SNAKE_CASE     :						float = 1.4							,						SCREAMING_SNAKE_CASE     :						float = -9.6			):







      '''simple docstring'''




      lowerCAmelCase  						=       0
      lowerCAmelCase  						=       first_x_coord
      lowerCAmelCase  						=       first_y_coord
      lowerCAmelCase  						=       (10.1 - point_y) / (0.0 - point_x)

      while not (-0.01 <= point_x <= 0.01 and point_y > 0):
            lowerCAmelCase						,		lowerCAmelCase						,		lowerCAmelCase  						=       next_point(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE			)
            num_reflections += 1

      return num_reflections


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













from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       )      ->				list[list[int]]:
   __snake_case							       =   []
   __snake_case							       =   []
   __snake_case							       =   0
   __snake_case							       =   sum(snake_case_       )
   create_state_space_tree(snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       )
   return result






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       ,      snake_case_	:  int       ,      snake_case_	:  list[int]       ,      snake_case_	:  list[list[int]]       ,      snake_case_	:  int       ,      )      ->				None:
   if sum(snake_case_       ) > max_sum or (remaining_nums_sum + sum(snake_case_       )) < max_sum:
      return
   if sum(snake_case_       ) == max_sum:
      result.append(snake_case_       )
      return
   for index in range(snake_case_       ,      len(snake_case_       )       ):
      create_state_space_tree(
          snake_case_       ,      snake_case_       ,      index + 1       ,      [*path, nums[index]]       ,      snake_case_       ,      remaining_nums_sum - nums[index]       ,      )
snake_case_				=			[3, 34, 4, 12, 5, 2]
snake_case_				=			9
snake_case_				=			generate_sum_of_subsets_soln(nums, max_sum)







print(*result)

