Manage Authentication Tokens with a Fixed Time to Live

## Problem Implement an authentication manager with a fixed `timeToLive`. `generate(tokenId, currentTime)` creates or replaces a token whose expiry is `currentTime + timeToLive`. `renew(tokenId, currentTime)` extends an existing token to `currentTime + timeToLive` only if it is still unexpired. `count(currentTime)` returns the number of unexpired tokens. Process operations in strictly increasing time order and return the result of each count operation. ### Constraints & Assumptions - There are at most 200,000 operations and `1 <= timeToLive <= 1,000,000,000`. - Every `currentTime` is an integer in `[1, 1,000,000,000,000]`, so every computed expiry is at most `1,001,000,000,000`, below `2^53`, and exactly representable across all four languages. - Token IDs are non-empty strings. - A token is expired when `currentTime >= expiryTime`. - Renewing a missing or expired token has no effect. ### Clarifications - Generating an existing token ID replaces its previous expiry. - Operation times are strictly increasing, so expired entries never become active again without generate. - Only count results are included in the returned list. ### Examples ```text timeToLive = 5 operations = [generate("a", 1), renew("a", 2), count(6), count(7)] output = [1, 0] ``` ### Hints ```hint Store authoritative expiry A map can tell whether a token's latest expiry is after the current time. ``` ```hint Discard stale expiration records If using an expiry-ordered queue, a token may have been renewed since an older queue item was created. ```