



from bisect import bisect
from itertools import accumulate


def 			UpperCamelCase(  __UpperCamelCase							:		Optional[int]     ,__UpperCamelCase							:		Optional[Any]     ,__UpperCamelCase							:		Dict     ,__UpperCamelCase							:		str ):
		lowerCAmelCase_			:     Union[str, Any]									= sorted(zip(__UpperCamelCase     ,__UpperCamelCase )     ,key=lambda __UpperCamelCase : x[0] / x[1]     ,reverse=__UpperCamelCase )
		lowerCAmelCase_					,  lowerCAmelCase_			:     Any									= [i[0] for i in r], [i[1] for i in r]
		lowerCAmelCase_			:     Union[str, Any]									= list(accumulate(__UpperCamelCase ) )
		lowerCAmelCase_			:     List[Any]									= bisect(__UpperCamelCase     ,__UpperCamelCase )
		return (
		    0
		    if k == 0
		    else sum(vl[:k] ) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
		    if k != n
		    else sum(vl[:k] )
		)


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 			UpperCamelCase(  ):
		lowerCAmelCase_			:     List[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=__UpperCamelCase     ,default=1     ,help='''Number of TPU cores to use (1 or 8).''' )

		# positional
		parser.add_argument(
		    '''training_script'''     ,type=__UpperCamelCase     ,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=__UpperCamelCase )

		return parser.parse_args()


def 			UpperCamelCase(  ):
		lowerCAmelCase_			:     str									= parse_args()

		# Import training_script as a module.
		lowerCAmelCase_			:     str									= Path(args.training_script )
		sys.path.append(str(script_fpath.parent.resolve() ) )
		lowerCAmelCase_			:     Tuple									= script_fpath.stem
		lowerCAmelCase_			:     Union[str, Any]									= importlib.import_module(__UpperCamelCase )

		# Patch sys.argv
		lowerCAmelCase_			:     Optional[int]									= [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()





