Design top-K frequency structure

Design an in-memory data structure that supports: add(x) to observe an item, inc(x) to increment its frequency, dec(x) to decrement (deleting when zero), and topK(k) to return the k items with highest frequency, breaking ties by most recent update. Target O( 1) amortized updates and O(k) retrieval using hash maps plus a doubly linked list of frequency buckets. Describe node layout, how buckets are created/merged, how recency is tracked, tie-breaking, memory bounds under churn, and concurrency considerations.