code: 
  
  def  _A  (			SCREAMING_SNAKE_CASE = 3_0			):
  	UpperCAmelCase__:  List[Any]		       =   exponent + 2
  	UpperCAmelCase__:  Dict		       =   (1 + 5**0.5) / 2
  	UpperCAmelCase__:  Union[str, Any]		       =   (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5
  
  	return int(SCREAMING_SNAKE_CASE			)
  
  
  if __name__ == "__main__":
  					print(F"{solution() = }")
style_context: 
  
  from __future__ import annotations
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	assert n > 1 and a > 0 and greatest_common_divisor(SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			) == 1
  	((UpperCAmelCase__)       ,	(UpperCAmelCase__)       ,	(UpperCAmelCase__)):  Optional[Any]		       =   extended_gcd(SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			)  # Implemented below
  	UpperCAmelCase__:  List[str]		       =   (b * s) % n
  	return x
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	((UpperCAmelCase__)       ,	(UpperCAmelCase__)):  int		       =   extended_euclid(SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			)  # Implemented below
  	if b < 0:
  		UpperCAmelCase__:  List[str]		       =   (b % n + n) % n
  	return b
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	UpperCAmelCase__:  Union[str, Any]		       =   invert_modulo(SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			)
  	UpperCAmelCase__:  Any		       =   (b * s) % n
  	return x
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	assert a >= 0 and b >= 0
  
  	if b == 0:
  		UpperCAmelCase__       ,	UpperCAmelCase__       ,	UpperCAmelCase__:  List[Any]		       =   a, 1, 0
  	else:
  		((UpperCAmelCase__)       ,	(UpperCAmelCase__)       ,	(UpperCAmelCase__)):  Tuple		       =   extended_gcd(SCREAMING_SNAKE_CASE  ,a % b			)
  		UpperCAmelCase__:  Union[str, Any]		       =   q
  		UpperCAmelCase__:  Union[str, Any]		       =   p - q * (a // b)
  
  	assert a % d == 0 and b % d == 0
  	assert d == a * x + b * y
  
  	return (d, x, y)
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	if b == 0:
  		return (1, 0)
  	((UpperCAmelCase__)       ,	(UpperCAmelCase__)):  List[str]		       =   extended_euclid(SCREAMING_SNAKE_CASE  ,a % b			)
  	UpperCAmelCase__:  Optional[Any]		       =   a // b
  	return (y, x - k * y)
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			):
  	if a < b:
  		UpperCAmelCase__       ,	UpperCAmelCase__:  str		       =   b, a
  
  	while a % b != 0:
  		UpperCAmelCase__       ,	UpperCAmelCase__:  Union[str, Any]		       =   b, a % b
  
  	return b
  
  
  if __name__ == "__main__":
  					from doctest import testmod
  
  					testmod(name="""modular_division""", verbose=True)
  					testmod(name="""modular_division2""", verbose=True)
  					testmod(name="""invert_modulo""", verbose=True)
  					testmod(name="""extended_gcd""", verbose=True)
  					testmod(name="""extended_euclid""", verbose=True)
  					testmod(name="""greatest_common_divisor""", verbose=True)