Problem $7($bonus question up to $10$ points; data structure and algorithm$)$ We are given a collection C of n integer keys $($where nis relatively large, say $1$ million$)$ that we can store however we like. We want to use this collection to answer queries of the form $$given a key k$($which may or may not be in C$),$ find all the keys in C that are at a distance d$0$ or less from k$,$ i$.$e$.,$ return the set $\{$k$$ in C:$|$k$$k$|$ d$\}($this is called a range search$).$Assume the collection is static, i$.$e$.,$ the n keys stay the same and we don$$t insert or delete any keys. Describe an efficient data structure for C and an algorithm to do many range searches$($no need to give pseudocode, but the description in English should be precise$).$ Give the runtime T$($n$)$ to set up the data structure, and the runtime S$($n$,$ m$)$ to do one range search assuming it returns m $$ n keys