Why do we always break down a query into prefix query when the problem involves Persistent Segment tree is it not possible to directly query a range [L,R]? For example consider this problem and the editorial — http://www.codechef.com/SNCKEL16/problems/SEGSUMQ

If we sort the vectors by the angle and then insert into the persistent segment tree in that order when we get a query <C,D> we can just query that segment tree in which all the vectors in it have lesser angle.

Am i missing something here? Could use some help. Thanks :)