Let T be a rooted tree. For a vertex set K $$ V $($T$)$ which contains the root node of T$,$

we define costT $($v$,$ K$)$ as the distance from v to the nearest ancestor of v in T contained

in K$.$ For instance, costT $($v$,$ K$)=0$ if v in K$,$ and costT $($v$,$ K$)=1$ if the parent of v is

in K$.$ Describe and analyze an algorithm that computing a smallest K $$ V $($T$)$ so that

max$\{$costT $($v$,$ K$)|$ v in V $($T$)\}<=$ r for a positive value r given as an input