
"""simple docstring"""

import importlib.metadata
import subprocess
import sys




def 			lowercase__  (    lowerCAmelCase :    Tuple = False       )       ->					Any:






    """simple docstring"""




    UpperCAmelCase  	=    False
    if "IPython" in sys.modules:
        UpperCAmelCase  	=    '''google.colab''' in str(sys.modules['IPython'].get_ipython()       )

    if in_colab:
        if upgrade:
            UpperCAmelCase  	=    ['''pip''', '''install''', '''-U''', '''torch''']
            subprocess.run(_lowercase       , check=_lowercase       )
        # get the current version of torch
        UpperCAmelCase  	=    importlib.metadata.version('torch'       )
        UpperCAmelCase  	=    torch_version[: torch_version.rindex('.'       )]
        UpperCAmelCase  	=    F"https://storage.googleapis.com/tpu-pytorch/wheels/colab/torch_xla-{torch_version_trunc}-cp37-cp37m-linux_x86_64.whl"
        UpperCAmelCase  	=    ['''pip''', '''install''', xla_wheel]
        subprocess.run(_lowercase       , check=_lowercase       )
    else:
        raise RuntimeError('`install_xla` utility works only on google colab.'       )










"""simple docstring"""




from functools import lru_cache





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



