Compute Cohort Retention Rate

You are given two tables: - `users(user_id BIGINT, signup_ts TIMESTAMP)` — one row per user. - `user_activity(user_id BIGINT, activity_ts TIMESTAMP, event_name VARCHAR)` — zero or more activity rows per user. Assume all timestamps are in UTC. Define a user's cohort as the calendar month of `signup_ts`. A user is retained in month `k` if they have at least one row in `user_activity` during the calendar month that is `k` months after their cohort month. Month `0` is the signup month. Write a SQL query to compute cohort-based monthly retention for `k = 0, 1, 2, 3, 4, 5, 6`. Return these columns: - `cohort_month` — first day of the signup month - `months_since_signup` — integer from 0 to 6 - `cohort_size` — number of users in the cohort - `retained_users` — number of distinct users active in that relative month - `retention_rate` — `retained_users / cohort_size` as a decimal Make sure each user is counted at most once per cohort-month and relative month.