


from __future__ import annotations

from collections.abc import Callable

_lowerCAmelCase:						Dict   				=       list[list[float | int]]






def   _lowercase(					__a				:						Matrix    ,     __a				:						Matrix     ):
							a__      =len(__a     )
							a__      =[[0 for _ in range(size + 1     )] for _ in range(__a     )]
							a__      =42
							a__      =42
							a__      =42
							a__      =42
							a__      =42
							a__      =42

							for row in range(__a     ):
														for col in range(__a     ):
																					a__      =matrix[row][col]

														a__      =vector[row][0]

							a__      =0
							a__      =0
							while row < size and col < size:
														# pivoting
														a__      =max((abs(augmented[rowa][col]     ), rowa) for rowa in range(__a    ,     __a     )     )[
														    1
														]
														if augmented[pivot_row][col] == 0:
																					col += 1
																					continue
														else:
																					a__    ,     a__      =augmented[pivot_row], augmented[row]

														for rowa in range(row + 1    ,     __a     ):
																					a__      =augmented[rowa][col] / augmented[row][col]
																					a__      =0
																					for cola in range(col + 1    ,     size + 1     ):
																												augmented[rowa][cola] -= augmented[row][cola] * ratio

														row += 1
														col += 1

							# back substitution
							for col in range(1    ,     __a     ):
														for row in range(__a     ):
																					a__      =augmented[row][col] / augmented[col][col]
																					for cola in range(__a    ,     size + 1     ):
																												augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
							return [
							    [round(augmented[row][size] / augmented[row][row]    ,     10     )] for row in range(__a     )
							]






def   _lowercase(					__a				:						list[int]     ):
							a__      =len(__a     )
							a__      =[[0 for _ in range(__a     )] for _ in range(__a     )]
							a__      =[[0] for _ in range(__a     )]
							a__      =42
							a__      =42
							a__      =42
							a__      =42

							for x_val, y_val in enumerate(__a     ):
														for col in range(__a     ):
																					a__      =(x_val + 1) ** (size - col - 1)
														a__      =y_val

							a__      =solve(__a    ,     __a     )

							def interpolated_func(__a				:						int     ) -> int:
														return sum(
														    round(coeffs[x_val][0]     ) * (var ** (size - x_val - 1))
														    for x_val in range(__a     )     )

							return interpolated_func






def   _lowercase(					__a				:						int     ):
							return (
							    1
							    - variable
							    + variable**2
							    - variable**3
							    + variable**4
							    - variable**5
							    + variable**6
							    - variable**7
							    + variable**8
							    - variable**9
							    + variable**10
							)






def   _lowercase(					__a				:						Callable[[int], int] = question_function    ,     __a				:						int = 10     ):
							a__      =[func(__a     ) for x_val in range(1    ,     order + 1     )]

							a__      =[
							    interpolate(data_points[:max_coeff]     ) for max_coeff in range(1    ,     order + 1     )
							]

							a__      =0
							a__      =42
							a__      =42

							for poly in polynomials:
														a__      =1
														while func(__a     ) == poly(__a     ):
																					x_val += 1

														ret += poly(__a     )

							return ret


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








from __future__ import annotations

def   __snake_case    (       _lowerCAmelCase			:			list[int]					,					_lowerCAmelCase			:			int						)			->    list[list[int]]:
   A_       :					list[list[int]]        =      []
   A_       :					list[int]        =      []
   A_       :					Dict        =      0
   A_       :					str        =      sum(_lowerCAmelCase						)
   create_state_space_tree(_lowerCAmelCase					,					_lowerCAmelCase					,					_lowerCAmelCase					,					_lowerCAmelCase					,					_lowerCAmelCase					,					_lowerCAmelCase						)
   return result

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





print(*result)
