I'm revisiting CSES problem set to help a friend. In "Sorting and Searching", there is this problem: Josephus Problem II. My solution was using an ordered set, and after a quick search, it seems like everyone online did this too. However, we see the more general version of this problem: List Removals in the section "Range Queries".

The category of this problem and a solution which is more general made me wonder if there is an alternative solution, perhaps without ordered set. I did some search online and found O(n) solution to the Josephus Problem (also see cp-algorithm). But this is different from the CSES problem, as it only finds the last element.

So, out of curiosity, is there any solution that is not doing removal on ordered set? Otherwise, this feels like a pretty bad problem.