'''simple docstring'''




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int				)    ->   int:
       while a != 0:
              lowercase_      :    Any       		= b % a, a
       return b




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int				)    ->   int:
       if gcd(UpperCAmelCase__   ,   UpperCAmelCase__				) != 1:
              lowercase_      :    Optional[Any]       		= F'''mod inverse of {a!r} and {m!r} does not exist'''
              raise ValueError(UpperCAmelCase__				)
       lowercase_      :    str       		= 1, 0, a
       lowercase_      :    Tuple       		= 0, 1, m
       while va != 0:
              lowercase_      :    List[Any]       		= ua // va
              lowercase_      :    int       		= (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
       return ua % m






'''simple docstring'''




from __future__ import annotations




def 							lowerCamelCase			(   UpperCAmelCase__ :      list   ,   UpperCAmelCase__ :      int | None = None   ,   UpperCAmelCase__ :      int | None = None				)    ->   None:
							if start is None:
														lowercase_      :    Any       		= 0

							if end is None:
														lowercase_      :    List[Any]       		= len(UpperCAmelCase__				) - 1

							if start >= end:
														return

							lowercase_      :    Optional[int]       		= (start + end) // 2

							slowsort(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)
							slowsort(UpperCAmelCase__   ,   mid + 1   ,   UpperCAmelCase__				)

							if sequence[end] < sequence[mid]:
														lowercase_		,		lowercase_      :    Dict       		= sequence[mid], sequence[end]

							slowsort(UpperCAmelCase__   ,   UpperCAmelCase__   ,   end - 1				)


if __name__ == "__main__":
						from doctest import testmod

						testmod()





