


'''simple docstring'''

import functools





def __snake_case      (   UpperCAmelCase_		:		str      ,       UpperCAmelCase_		:		str					):
 lowerCamelCase_  				=						len(UpperCAmelCase_					)
 lowerCamelCase_  				=						len(UpperCAmelCase_					)

 @functools.cache
 def min_distance(UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int					) -> int:
  # if first word index is overflow - delete all from the second word
  if indexa >= len_worda:
   return len_worda - indexa
  # if second word index is overflow - delete all from the first word
  if indexa >= len_worda:
   return len_worda - indexa
  lowerCamelCase_  				=						int(worda[indexa] != worda[indexa]					)  # current letters not identical
  return min(
      1 + min_distance(indexa + 1      ,       UpperCAmelCase_					)      ,       1 + min_distance(UpperCAmelCase_      ,       indexa + 1					)      ,       diff + min_distance(indexa + 1      ,       indexa + 1					)      ,       )

 return min_distance(0      ,       0					)


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)



