






import warnings

from .generation import GenerationMixin
class 							__snake_case(       _snake_case   ):
 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.'''  ,							_snake_case  ,							)







from __future__ import annotations





def 		__snake_case						(    _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase				):
					"""simple docstring"""






					assert (
					    c % greatest_common_divisor(_UpperCAmelCase       ,			_UpperCAmelCase				) == 0
					)  # greatest_common_divisor(a,b) function implemented below
					((lowercase)   ,      (lowercase)   ,      (lowercase))						   =       extended_gcd(_UpperCAmelCase       ,			_UpperCAmelCase				)  # extended_gcd(a,b) function implemented below
					lowercase						   =       c / d
					return (r * x, r * y)





def 		__snake_case						(    _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase = 2				):
					"""simple docstring"""






					((lowercase)   ,      (lowercase))						   =       diophantine(_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase				)  # Initial value
					lowercase						   =       greatest_common_divisor(_UpperCAmelCase       ,			_UpperCAmelCase				)
					lowercase						   =       a // d
					lowercase						   =       b // d

					for i in range(_UpperCAmelCase				):
										lowercase						   =       xa + i * q
										lowercase						   =       ya - i * p
										print(_UpperCAmelCase       ,			_UpperCAmelCase				)





def 		__snake_case						(    _UpperCAmelCase       ,			_UpperCAmelCase				):
					"""simple docstring"""






					if a < b:
										lowercase   ,      lowercase						   =       b, a

					while a % b != 0:
										lowercase   ,      lowercase						   =       b, a % b

					return b





def 		__snake_case						(    _UpperCAmelCase       ,			_UpperCAmelCase				):
					"""simple docstring"""






					assert a >= 0 and b >= 0

					if b == 0:
										lowercase   ,      lowercase   ,      lowercase						   =       a, 1, 0
					else:
										((lowercase)   ,      (lowercase)   ,      (lowercase))						   =       extended_gcd(_UpperCAmelCase       ,			a % b				)
										lowercase						   =       q
										lowercase						   =       p - q * (a // b)

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

					return (d, x, y)


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

		testmod(name='''diophantine''', verbose=True)
		testmod(name='''diophantine_all_soln''', verbose=True)
		testmod(name='''extended_gcd''', verbose=True)
		testmod(name='''greatest_common_divisor''', verbose=True)






