Reschedule Meetings for Maximum Free Time I

Represent the schedule by its free gaps: before the first meeting, between every adjacent pair, and after the final meeting until eventTime. If meetings stay in order and up to k meetings can be moved, moving a consecutive block of k meetings can join the k + 1 surrounding gaps into one free interval. Therefore compute each gap and find the maximum sum over every contiguous window of k + 1 gaps. Initialize the first window, then slide it by adding the entering gap and subtracting the leaving gap.

This works because no unaffected meeting can sit inside the resulting uninterrupted free time; the meetings removed from its interior must form one consecutive block. Conversely, any consecutive block can be relocated into existing available time under the problem's stated feasibility guarantee, leaving its surrounding gaps connected. Test k = 0, moving all meetings, zero-length gaps from touching meetings, one meeting, and free time at either event boundary. Building gaps and scanning the window both take O(n) time; the answer can be computed in O(1) extra space beyond the input or O(n) if gaps are materialized.