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Kestrel Stream needs the longest session that touches at most two categories, and the number of sessions that touch exactly two. The first attempt extends from every start and needs about a trillion steps on the worst night. One window that only moves forward finds the longest in O(n), adding right minus left plus one counts every valid session, and exactly K is at most K minus at most K minus 1.
Kestrel Stream tags every play with a content category.