I was doing this question Hotel Queries on CSES. I understand the obvious Nlog^2N approach that uses binary search on segment trees.

But I'm interested in solving it in NlogN and I know the fractional cascading approach that traverses the segment tree. But I want to try this approach on an iterative segment tree ,exactly the same implement as in the blog Efficient and easy segment trees.

But apparently the tree from this version of the segment tree is degenerate where we cannot guarantee that the left child corresponds to an actual left range. i.e it is not necessary for the left child to have range [l1,r1] such that r1>l2 for the corresponding right child.

Please share any implementations of fractional cascading or any NlogN approaches you know using iterative segment tree for the problem.