


from functools import lru_cache






@lru_cache
def 		lowercase_(  SCREAMING_SNAKE_CASE_     ):


  '''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 		lowercase_(  SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  lowerCamelCase			: List[str]   =    len(SCREAMING_SNAKE_CASE_     )
  # Find m such that F_m >= n where F_i is the i_th fibonacci number.
  lowerCamelCase			: Dict   =    0
  while True:
    if fibonacci(SCREAMING_SNAKE_CASE_     ) >= len_list:
      lowerCamelCase			: int   =    i
      break
    i += 1
  lowerCamelCase			: List[str]   =    0
  while fibb_k > 0:
    lowerCamelCase			: Dict   =    min(
        offset + fibonacci(fibb_k - 1     )				,						len_list - 1     )  # Prevent out of range
    lowerCamelCase			: Optional[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 importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: str   =    ArgumentParser(
      description=(
          "PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"
      )     )

  # Optional arguments for the launch helper
  parser.add_argument("--num_cores"				,						type=SCREAMING_SNAKE_CASE_				,						default=1				,						help="Number of TPU cores to use (1 or 8)."     )

  # positional
  parser.add_argument(
      "training_script"				,						type=SCREAMING_SNAKE_CASE_				,						help=(
          "The full path to the single TPU training "
          "program/script to be launched in parallel, "
          "followed by all the arguments for the "
          "training script"
      )				,						)

  # rest from the training program
  parser.add_argument("training_script_args"				,						nargs=SCREAMING_SNAKE_CASE_     )

  return parser.parse_args()






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: Optional[Any]   =    parse_args()

  # Import training_script as a module.
  lowerCamelCase			: Tuple   =    Path(args.training_script     )
  sys.path.append(str(script_fpath.parent.resolve()     )     )
  lowerCamelCase			: int   =    script_fpath.stem
  lowerCamelCase			: Tuple   =    importlib.import_module(SCREAMING_SNAKE_CASE_     )

  # Patch sys.argv
  lowerCamelCase			: Union[str, Any]   =    [args.training_script] + args.training_script_args + ["--tpu_num_cores", str(args.num_cores     )]

  xmp.spawn(mod._mp_fn				,						args=()				,						nprocs=args.num_cores     )


if __name__ == "__main__":
   main()



