


from __future__ import annotations



def 	_lowerCAmelCase  (							lowerCAmelCase_							:list[int]						,  lowerCAmelCase_							:int							)->list[list[int]]:
   '''simple docstring'''






   snake_case_    			=    []
   snake_case_    			=    []
   snake_case_    			=    0
   snake_case_    			=    sum(SCREAMING_SNAKE_CASE_							)
   create_state_space_tree(SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_							)
   return result



def 	_lowerCAmelCase  (							lowerCAmelCase_							:list[int]						,  lowerCAmelCase_							:int						,  lowerCAmelCase_							:int						,  lowerCAmelCase_							:list[int]						,  lowerCAmelCase_							:list[list[int]]						,  lowerCAmelCase_							:int						,  )->None:
   '''simple docstring'''






   if sum(SCREAMING_SNAKE_CASE_							) > max_sum or (remaining_nums_sum + sum(SCREAMING_SNAKE_CASE_							)) < max_sum:
      return
   if sum(SCREAMING_SNAKE_CASE_							) == max_sum:
      result.append(SCREAMING_SNAKE_CASE_							)
      return
   for index in range(SCREAMING_SNAKE_CASE_						,  len(SCREAMING_SNAKE_CASE_							)							):
      create_state_space_tree(
          SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  index + 1						,  [*path, nums[index]]						,  SCREAMING_SNAKE_CASE_						,  remaining_nums_sum - nums[index]						,  )
SCREAMING_SNAKE_CASE		:Any     						=   [3, 34, 4, 12, 5, 2]
SCREAMING_SNAKE_CASE		:Dict     						=   9
SCREAMING_SNAKE_CASE		:List[Any]     						=   generate_sum_of_subsets_soln(nums, max_sum)



print(*result)








"""simple docstring"""




from math import isclose, sqrt


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float  )   ->						tuple[float, float, float]:
						SCREAMING_SNAKE_CASE													=					point_y / 4 / point_x
						SCREAMING_SNAKE_CASE													=					2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						SCREAMING_SNAKE_CASE													=					(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						SCREAMING_SNAKE_CASE													=					(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
						SCREAMING_SNAKE_CASE													=					outgoing_gradient**2 + 4
						SCREAMING_SNAKE_CASE													=					2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						SCREAMING_SNAKE_CASE													=					(point_y - outgoing_gradient * point_x) ** 2 - 1_00

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

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

						return next_x, next_y, outgoing_gradient


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float = 1.4 ,			SCREAMING_SNAKE_CASE_		:				float = -9.6  )   ->						int:
						SCREAMING_SNAKE_CASE													=					0
						SCREAMING_SNAKE_CASE													=					first_x_coord
						SCREAMING_SNAKE_CASE													=					first_y_coord
						SCREAMING_SNAKE_CASE													=					(10.1 - point_y) / (0.0 - point_x)

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

						return num_reflections


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


