






"""simple docstring"""

from math import loga






def _lowerCAmelCase	(  __lowerCamelCase:int   ):

						'''simple docstring'''






						if a < 0:
												raise ValueError("Input value must be a positive integer"   )
						elif isinstance(__lowerCamelCase ,						__lowerCamelCase   ):
												raise TypeError("Input value must be a 'int' type"   )
						return 0 if (a == 0) else int(loga(a & -a   )   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()











"""simple docstring"""

from __future__ import annotations

from random import choice






def _lowerCAmelCase	(  __lowerCamelCase:Optional[int]   ):

						'''simple docstring'''






						return choice(__lowerCamelCase   )






def _lowerCAmelCase	(  __lowerCamelCase:list[int] ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     random_pivot(__lowerCamelCase   )

						# partition based on pivot
						# linear time
						__magic_name__            =     [e for e in lst if e < pivot]
						__magic_name__            =     [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(__lowerCamelCase   ) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(__lowerCamelCase   ) < k - 1:
												return kth_number(__lowerCamelCase ,						k - len(__lowerCamelCase   ) - 1   )
						# pivot is in elements smaller than k
						else:
												return kth_number(__lowerCamelCase ,						__lowerCamelCase   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()



