



from __future__ import annotations

from typing import Any

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list[Any]    ):
				"""simple docstring"""







				create_state_space_tree(_SCREAMING_SNAKE_CASE				,     []				,     0    )

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list[Any]				,     _SCREAMING_SNAKE_CASE       :			list[Any]				,     _SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







				if index == len(_SCREAMING_SNAKE_CASE    ):
								print(_SCREAMING_SNAKE_CASE    )
								return

				create_state_space_tree(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE				,     index + 1    )
				current_subsequence.append(sequence[index]    )
				create_state_space_tree(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE				,     index + 1    )
				current_subsequence.pop()


if __name__ == "__main__":
						lowerCamelCase__			= [3, 1, 2, 4]
						generate_all_subsequences(seq)

						seq.clear()
						seq.extend(["""A""", """B""", """C"""])
						generate_all_subsequences(seq)





def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			int = 3				,     _SCREAMING_SNAKE_CASE       :			int = 7				,     _SCREAMING_SNAKE_CASE       :			int = 100_0000    ):
				"""simple docstring"""







				__a       =		0
				__a       =		1

				for current_denominator in range(1				,     limit + 1    ):
								__a       =		current_denominator * numerator // denominator
								if current_denominator % denominator == 0:
												current_numerator -= 1
								if current_numerator * max_denominator > current_denominator * max_numerator:
												__a       =		current_numerator
												__a       =		current_denominator
				return max_numerator


if __name__ == "__main__":
						print(solution(numerator=3, denominator=7, limit=100_0000))
