## Problem Implement `outside_coverage(providers, clients, max_distance)`. Each provider has an `id`, a list of `specialties`, and a two-dimensional `location = [x, y]`. Each client has an `id`, a list of required specialties in `requirements`, and a two-dimensional location. A required specialty is covered when at least one provider offering that specialty is within Euclidean distance `max_distance` of the client. Different requirements may be covered by different providers. Return the IDs of clients for which at least one required specialty is not covered. Preserve client input order. ## Constraints - Up to `2,000` providers and `2,000` clients - Coordinates and `max_distance` are finite numbers; `max_distance >= 0` - Specialty strings within one record are unique. - Multiple providers or clients may share a location. - Distance exactly equal to `max_distance` is covered. ## Example Providers: ```text P1: specialties=[cardio, ortho], location=[0, 0] P2: specialties=[pedi], location=[5, 0] ``` Clients: ```text C1: requirements=[ortho], location=[1, 0] C2: requirements=[ortho, pedi], location=[1, 0] C3: requirements=[pedi], location=[4, 0] ``` With `max_distance = 2`, return `[C2]`. ## Hint Compare squared distances to avoid unnecessary square roots. Correctness requires checking every required specialty, not merely finding one nearby provider. ## Interview Follow-ups - Index providers to support many repeated queries. - Explain how the design changes in geographic coordinates rather than a flat plane. - Return the missing specialties for each uncovered client.