K-th Nearest Obstacle Queries

Given a stream of point insertions on an infinite plane, after each insertion return the k-th smallest Manhattan distance (|x|+|y|) from the origin or -1 if fewer than k points exist. The core challenge is to maintain the k-th order statistic of distances under insert-only updates efficiently (e.g., with a size-k heap or other order-statistic structure) for up to 2e5 queries.