Fix the join audit for a Spark job

An AI agent wrote a Spark job that inner-joins clickstream events to a user table, with a broadcast hint, and writes the output partitioned by date. Before review you want three facts you can defend: how many events the join drops, whether the broadcast is safe, and how many date partitions the output lands in.

An assistant wrote audit_spark_join(event_user_ids, event_dates, dim_user_ids, dim_size_mb, broadcast_limit_mb). It is in the editor. It has a bug. Find it and fix it.

Input and output:

• event_user_ids, event_dates: two lists of the same length. Event i belongs to user event_user_ids[i] and happened on event_dates[i].
• dim_user_ids: the user ids in the user table. Ids may repeat.
• dim_size_mb, broadcast_limit_mb: the user table's size and the largest table the cluster will broadcast, in MB.
• Return exactly three strings, in this order: "dropped=<n>", "broadcast=<safe or unsafe>", "partitions=<k>".

Rules the tests check:

• An event survives the join when its user id appears in dim_user_ids, compared exactly. The empty string is an ordinary id.
• n is the number of event rows that do not survive. Every row counts, so two events from the same missing user count as 2.
• The broadcast is safe when dim_size_mb is less than or equal to broadcast_limit_mb, else unsafe.
• k is the number of distinct dates among the surviving events only.