






def  a__ (__lowercase							:Tuple					,  __lowercase							:int					,  __lowercase							:Union[str, Any]   )		-> Optional[int]:
				if n == 0:
								return 1

				elif n % 2 == 1:
								return (binary_exponentiation(__lowercase					,  n - 1					,  __lowercase   ) * a) % mod

				else:
								_A	:				Any   =      binary_exponentiation(__lowercase					,  n / 2					,  __lowercase   )
								return (b * b) % mod


# a prime number
_UpperCamelCase			:	Tuple								=701

_UpperCamelCase			:	int								=1000000000
_UpperCamelCase			:	Tuple								=10

# using binary exponentiation function, O(log(p)):
print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p)






print((a / b) % p == (a * b ** (p - 2)) % p)











import warnings


warnings.warn(
    'memory_utils has been reorganized to utils.memory. Import `find_executable_batchsize` from the main `__init__`: '
    '`from accelerate import find_executable_batch_size` to avoid this warning.',
    FutureWarning,
)



