Define users as “new” during the first 30 days inclusive after their signup_date, and “old” thereafter. Produce per-user, per-day labels over a window, acknowledging that a single user naturally has different labels on different days. Use today = 2025-09-01. Schema: users(user_id INT, signup_date DATE) activity(user_id INT, activity_date DATE) -- any daily activity counts as presence Sample data: users +---------+-------------+ | user_id | signup_date | +---------+-------------+ | 1 | 2025-07-25 | | 2 | 2025-08-20 | | 3 | 2025-08-01 | | 4 | 2025-09-01 | +---------+-------------+ activity +---------+---------------+ | user_id | activity_date | +---------+---------------+ | 1 | 2025-08-02 | | 1 | 2025-08-26 | | 2 | 2025-08-25 | | 2 | 2025-09-01 | | 3 | 2025-08-15 | | 3 | 2025-09-01 | | 4 | 2025-09-01 | +---------+---------------+ Tasks: A) Write SQL that outputs (user_id, d, label) for every day d in [2025-08-02, 2025-09-01], labeling “new” if d between signup_date and signup_date + 29 days inclusive, else “old”. Avoid assigning multiple labels for the same user-day. Prefer generating dates only where activity exists (join to activity) to reduce scan cost. B) Using your labels, compute two aggregates for the last 30 days relative to today (window = [2025-08-03, 2025-09-01]): (i) active_new_users and active_old_users per day; (ii) a single summary row with total distinct users by label over the window. Explain any assumptions about time zones and inclusive/exclusive bounds.