Design and implement a topic-based news subscription service for a news aggregation platform. Provide a class NewsProvider supporting the following operations and constraints: Operations - AddSubscription(subscriberId, minInterest, maxNewsPerSecond, topics) -> bool • Create or update a subscriber’s configuration. • Return true on success; return false on invalid input or violated constraints. - RemoveSubscription(subscriberId) -> bool • Remove a subscriber; return false if the subscriberId does not exist. - NewsReceived(newsId, timestamp, interest, topics) -> bool • Ingest a news item with its timestamp, interest score, and topics. • Return false if newsId already exists; otherwise true. - Publish(nowTimestamp, maxAge) -> dict[int, list[int]] • For each subscriber, return the list of newsIds to deliver at nowTimestamp, subject to the rules below. Publish rules - Eligibility: news interest ≥ subscriber.minInterest. - Topic filter: news topics intersect subscriber.topics. - Freshness: nowTimestamp - maxAge ≤ news.timestamp ≤ nowTimestamp. - Rate limiting: per-subscriber sliding window allowing at most maxNewsPerSecond items in any 1-second rolling window. - De-duplication: the same newsId must not be delivered to the same subscriber more than once. - Ordering: higher interest first; if ties, older timestamp first; if still tied, smaller newsId first. Deliverables - Specify data structures for: subscriptions, news storage, delivered-tracking per subscriber, and per-subscriber sliding-window counters. - Describe algorithms for filtering, rate limiting (sliding window), de-duplication, and multi-key sorting under high throughput. - Analyze time and space complexity of each operation and Publish. - Discuss concurrency, idempotency, and persistence considerations. - Explain how you would scale this to millions of users and a large, continuous news stream (partitioning, sharding, backpressure, batching, and fault tolerance).