users(user_id, signup_at) and events(user_id, event_type, event_at)

For each signup month report the cohort size, the percentage of users who completed a 'profile' event after signing up, and the percentage who completed a 'first_purchase' event after their profile event.

Return signup_month as 'YYYY-MM', cohort_size, profile_pct and purchase_after_profile_pct, both rounded to two decimals, ordered by month. Both percentages are out of the whole cohort.

A purchase that happened before the profile does not count, so the purchase check has to be anchored to the profile timestamp rather than to signup.

Tables

events

user_id  event_type      event_at
-------  --------------  -------------------
1        profile         2026-01-06 10:00:00
1        first_purchase  2026-01-08 10:00:00
2        first_purchase  2026-01-11 10:00:00
2        profile         2026-01-12 10:00:00
3        profile         2026-01-19 10:00:00
4        profile         2026-02-03 10:00:00
4        first_purchase  2026-02-09 10:00:00

users

user_id  signup_at
-------  -------------------
1        2026-01-05 10:00:00
2        2026-01-10 10:00:00
3        2026-01-20 10:00:00
4        2026-02-02 10:00:00

Expected result

signup_month  cohort_size  profile_pct  purchase_after_profile_pct
------------  -----------  -----------  --------------------------
2026-01       3            66.67        33.33
2026-02       1            100.00       100.00