Implement build_sessions(events, gap), which groups a user event log into sessions.

Input

events = [("A", 1), ("A", 2), ("A", 10), ("A", 11), ("B", 3)]

Tuples of (user, timestamp). They are not guaranteed to be sorted — one user's events may arrive interleaved and out of order.

Rules

• Sort each user's timestamps ascending, then cut them into sessions.
• Break a session when the gap between two consecutive events is greater than gap (> gap). A gap of exactly gap stays in the same session.
• Duplicate timestamps each remain their own event.

Output

build_sessions(events, gap=5)
# {"A": [[1, 2], [10, 11]], "B": [[3]]}

• User keys keep their order of first appearance in the input (not sorted time order).
• Each session is a list of timestamps in ascending order.
• Empty input returns an empty dictionary.

Implement build_sessions(events, gap). gap is an integer of 0 or more.