





"""simple docstring"""





from functools import lru_cache




@lru_cache
def 		lowerCAmelCase_     (  lowercase_       :							int		):

 '''simple docstring'''






 if not isinstance(lowercase_			,				lowercase_		):
  raise TypeError('''k must be an integer.'''		)
 if k < 0:
  raise ValueError('''k integer must be greater or equal to zero.'''		)
 if k == 0:
  return 0
 elif k == 1:
  return 1
 else:
  return fibonacci(k - 1		) + fibonacci(k - 2		)




def 		lowerCAmelCase_     (  lowercase_       :							list			,				lowercase_       :							int		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      int 							=	len(lowercase_		)
 # Find m such that F_m >= n where F_i is the i_th fibonacci number.
 __SCREAMING_SNAKE_CASE			:      Dict 							=	0
 while True:
  if fibonacci(lowercase_		) >= len_list:
   __SCREAMING_SNAKE_CASE			:      str 							=	i
   break
  i += 1
 __SCREAMING_SNAKE_CASE			:      Tuple 							=	0
 while fibb_k > 0:
  __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	min(
      offset + fibonacci(fibb_k - 1		)			,				len_list - 1		)  # Prevent out of range
  __SCREAMING_SNAKE_CASE			:      str 							=	arr[index_k]
  if item_k_1 == val:
   return index_k
  elif val < item_k_1:
   fibb_k -= 1
  elif val > item_k_1:
   offset += fibonacci(fibb_k - 1		)
   fibb_k -= 2
 else:
  return -1


if __name__ == "__main__":
    import doctest

    doctest.testmod()








"""simple docstring"""





from ..utils import DummyObject, requires_backends





class       snake_case		(       metaclass=__UpperCAmelCase       ):
      lowerCamelCase__      =			['''torch''', '''transformers''', '''invisible_watermark''']

      def __init__(      self       :Optional[int]						,							*_lowerCamelCase       :int						,							**_lowerCamelCase       :Any						):
       requires_backends(self						,							['''torch''', '''transformers''', '''invisible_watermark''']						)

      @classmethod
      def 						SCREAMING_SNAKE_CASE_      (      cls       :Dict						,							*_lowerCamelCase       :Optional[Any]						,							**_lowerCamelCase       :int						):
       requires_backends(cls						,							['''torch''', '''transformers''', '''invisible_watermark''']						)



      @classmethod
      def 						SCREAMING_SNAKE_CASE_      (      cls       :Optional[int]						,							*_lowerCamelCase       :Optional[Any]						,							**_lowerCamelCase       :Union[str, Any]						):
       requires_backends(cls						,							['''torch''', '''transformers''', '''invisible_watermark''']						)







class       snake_case		(       metaclass=__UpperCAmelCase       ):
      lowerCamelCase__      =			['''torch''', '''transformers''', '''invisible_watermark''']

      def __init__(      self       :Dict						,							*_lowerCamelCase       :Dict						,							**_lowerCamelCase       :Optional[Any]						):
       requires_backends(self						,							['''torch''', '''transformers''', '''invisible_watermark''']						)

      @classmethod
      def 						SCREAMING_SNAKE_CASE_      (      cls       :Optional[int]						,							*_lowerCamelCase       :int						,							**_lowerCamelCase       :Optional[int]						):
       requires_backends(cls						,							['''torch''', '''transformers''', '''invisible_watermark''']						)



      @classmethod
      def 						SCREAMING_SNAKE_CASE_      (      cls       :List[Any]						,							*_lowerCamelCase       :Dict						,							**_lowerCamelCase       :List[str]						):
       requires_backends(cls						,							['''torch''', '''transformers''', '''invisible_watermark''']						)

