

from functools import lru_cache







@lru_cache
def _a					(			SCREAMING_SNAKE_CASE						:     int						)       ->       int:

 """simple docstring"""






 if not isinstance(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						):
  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 _a					(			SCREAMING_SNAKE_CASE						:     list       ,   SCREAMING_SNAKE_CASE						:     int						)       ->       int:

 """simple docstring"""






 __lowerCAmelCase:  Optional[Any]        = len(SCREAMING_SNAKE_CASE						)
 # Find m such that F_m >= n where F_i is the i_th fibonacci number.
 __lowerCAmelCase:  Optional[Any]        = 0
 while True:
  if fibonacci(SCREAMING_SNAKE_CASE						) >= len_list:
   __lowerCAmelCase:  Dict        = i
   break
  i += 1
 __lowerCAmelCase:  str        = 0
 while fibb_k > 0:
  __lowerCAmelCase:  Union[str, Any]        = min(
      offset + fibonacci(fibb_k - 1						)       ,   len_list - 1						)  # Prevent out of range
  __lowerCAmelCase:  int        = 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()








import numpy as np







def _a					(			SCREAMING_SNAKE_CASE						:     Union[str, Any]						)       ->       List[str]:

 """simple docstring"""






 __lowerCAmelCase:  Union[str, Any]        = np.exp(SCREAMING_SNAKE_CASE						)

 # Add up the all the exponentials
 __lowerCAmelCase:  Dict        = np.sum(SCREAMING_SNAKE_CASE						)

 # Divide every exponent by the sum of all exponents
 __lowerCAmelCase:  int        = exponent_vector / sum_of_exponents

 return softmax_vector


if __name__ == "__main__":
  print(softmax((0,)))





