Paginate forward and backward through results

You are asked to extend a basic pagination system to support **forward** and **backward** navigation, similar to a cursor-based API. You are given: - A zero-indexed array of items `items` sorted in a fixed, deterministic order. - An integer `pageSize > 0`. Design a paginator with the following operations: 1. `getFirstPage()` → returns the first `pageSize` items and a **cursor** representing the position after the last returned item. 2. `getNextPage(cursor)` → given a cursor returned by a previous call, return the next `pageSize` items and a new cursor. If there are no more items, return an empty list and a special "end" cursor. 3. `getPrevPage(cursor)` → given a cursor, return the **previous** page of `pageSize` items and a new cursor pointing to the start of that page. If there is no previous page, return an empty list and a "start" cursor. Requirements: - Define what the cursor contains (it could just be an index or a more complex token). - All operations should run in **O(pageSize)** time. - Handle edge cases correctly, including: - Moving past the last page with `getNextPage`. - Moving before the first page with `getPrevPage`. - Cases where `len(items)` is not a multiple of `pageSize`. Implement the data structure and its methods with clear handling of indices and cursors.