Design and implement a precise sliding-window rate limiter for an API. Part A: Enforce a global cap of R requests within any rolling T-second window (true sliding window, not fixed window or token bucket). Specify the public interface, data structures, time resolution, and time/space complexity. Part B: Each request includes userId and userExperience fields. Enforce independent limits per userId and per userExperience concurrently (e.g., U requests per T seconds per userId and X requests per T seconds per userExperience). Explain key design choices: how to structure keys/counters to support multiple dimensions without double-counting; how to evict stale state efficiently; how to deploy and scale this in a distributed environment (sharding, coordination, clock skew, idempotency); and how you would test correctness and edge cases (bursts, boundary timestamps, window rollover).