



from __future__ import annotations


def    __lowerCamelCase   (  lowerCamelCase__	,					lowerCamelCase__		):

				"""simple docstring"""


				lowercase__	:       Optional[int]						=	[]
				lowercase__	:       int						=	[]
				lowercase__	:       Dict						=	0
				lowercase__	:       Tuple						=	sum(lowerCAmelCase__		)
				create_state_space_tree(lowerCAmelCase__	,					lowerCAmelCase__	,					lowerCAmelCase__	,					lowerCAmelCase__	,					lowerCAmelCase__	,					lowerCAmelCase__		)
				return result


def    __lowerCamelCase   (  lowerCamelCase__	,					lowerCamelCase__	,					lowerCamelCase__	,					lowerCamelCase__	,					lowerCamelCase__	,					lowerCamelCase__	,					):

				"""simple docstring"""


				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__	    =    [3, 3_4, 4, 1_2, 5, 2]
lowerCAmelCase__	    =    9
lowerCAmelCase__	    =    generate_sum_of_subsets_soln(nums, max_sum)
print(*result)





"""simple docstring"""






import math


def      UpperCAmelCase__			(							lowerCAmelCase__	:int						)					->       bool:
      '''simple docstring'''


      lowercase								=      math.loga(math.sqrt(4 * positive_integer + 1						) / 2 + 1 / 2						)

      return exponent == int(lowerCAmelCase__						)


def      UpperCAmelCase__			(							lowerCAmelCase__	:float = 1 / 1_2_3_4_5						)					->       int:
      '''simple docstring'''


      lowercase								=      0
      lowercase								=      0

      lowercase								=      3
      while True:
            lowercase								=      (integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(lowerCAmelCase__						):
                  lowercase								=      int(lowerCAmelCase__						)
                  total_partitions += 1
                  if check_partition_perfect(lowerCAmelCase__						):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(lowerCAmelCase__						)
            integer += 1


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



