


'''simple docstring'''

def __snake_case      (   UpperCAmelCase_		:		int	):
 assert (
     isinstance(UpperCAmelCase_      ,       UpperCAmelCase_	) and number_of_steps > 0
 ), F'''number_of_steps needs to be positive integer, your input {number_of_steps}'''
 if number_of_steps == 1:
  return 1
 lowerCamelCase_				,lowerCamelCase_  				=						1, 1
 for _ in range(number_of_steps - 1	):
  lowerCamelCase_				,lowerCamelCase_  				=						current + previous, current
 return current


if __name__ == "__main__":
     import doctest

     doctest.testmod()







'''simple docstring'''

from __future__ import annotations





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 if b == 0:
  return (1, 0)
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       a % b	)
 lowerCamelCase_  				=						a // b
 return (y, x - k * y)





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 if b < 0:
  lowerCamelCase_  				=						(b % n + n) % n
 return b





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 lowerCamelCase_				,lowerCamelCase_  				=						invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	), invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m


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

     testmod(name="""chinese_remainder_theorem""", verbose=True)
     testmod(name="""chinese_remainder_theorem2""", verbose=True)
     testmod(name="""invert_modulo""", verbose=True)
     testmod(name="""extended_euclid""", verbose=True)



