






from __future__ import annotations







def 						a_      (__A							,					__A							,					__A			)							->	int:



     """simple docstring"""
     assert n > 1 and a > 0 and greatest_common_divisor(__A							,					__A			) == 1
     ((__a)			, (__a)			, (__a))				:	Union[str, Any]			=				extended_gcd(__A							,					__A			)  # Implemented below
     __a				:	Any			=				(b * s) % n
     return x







def 						a_      (__A							,					__A			)							->	int:



     """simple docstring"""
     ((__a)			, (__a))				:	Optional[int]			=				extended_euclid(__A							,					__A			)  # Implemented below
     if b < 0:
          __a				:	Union[str, Any]			=				(b % n + n) % n
     return b







def 						a_      (__A							,					__A							,					__A			)							->	int:



     """simple docstring"""
     __a				:	Optional[Any]			=				invert_modulo(__A							,					__A			)
     __a				:	Any			=				(b * s) % n
     return x







def 						a_      (__A							,					__A			)							->	tuple[int, int, int]:



     """simple docstring"""
     assert a >= 0 and b >= 0

     if b == 0:
          __a			, __a			, __a				:	str			=				a, 1, 0
     else:
          ((__a)			, (__a)			, (__a))				:	Dict			=				extended_gcd(__A							,					a % b			)
          __a				:	Optional[int]			=				q
          __a				:	Optional[int]			=				p - q * (a // b)

     assert a % d == 0 and b % d == 0
     assert d == a * x + b * y

     return (d, x, y)







def 						a_      (__A							,					__A			)							->	tuple[int, int]:



     """simple docstring"""







     if b == 0:
          return (1, 0)
     ((__a)			, (__a))				:	int			=				extended_euclid(__A							,					a % b			)
     __a				:	List[Any]			=				a // b
     return (y, x - k * y)







def 						a_      (__A							,					__A			)							->	int:



     """simple docstring"""







     if a < b:
          __a			, __a				:	Tuple			=				b, a

     while a % b != 0:
          __a			, __a				:	str			=				b, a % b

     return b


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

   testmod(name='''modular_division''', verbose=True)
   testmod(name='''modular_division2''', verbose=True)
   testmod(name='''invert_modulo''', verbose=True)
   testmod(name='''extended_gcd''', verbose=True)
   testmod(name='''extended_euclid''', verbose=True)
   testmod(name='''greatest_common_divisor''', verbose=True)













import warnings

from .generation import GenerationMixin




class        snake_case_					(						__UpperCamelCase			):

						"""simple docstring"""



						warnings.warn(
						    """Importing `GenerationMixin` from `src/transformers/generation_utils.py` is deprecated and will """
						    """be removed in Transformers v5. Import as `from transformers import GenerationMixin` instead."""		,       __UpperCamelCase		,       )





