The Rift-Sigils of Corvanthe Chasm

Along the lip of Corvanthe Chasm runs a single line of carved sigils, older than any road in the province. The Order of the Grey Lectern posts a bounty for a binder who can read the longest unbroken stretch of them in one sitting. A binder's mind can hold only so many *kinds* of sigil at once. A kind may appear any number of times within the stretch without costing anything extra.

Write longestBinding(sigils, k).

• sigils is a list of strings, in order along the chasm wall. Each string names the kind of one sigil. Two sigils are the same kind exactly when their strings are equal, and the comparison is case-sensitive.
• k is a non-negative integer: the most distinct kinds the binder can hold.

Return an integer: the length of the longest contiguous run of sigils (consecutive elements, in their given order) that contains at most k distinct strings. If no non-empty run qualifies, return 0. This includes the case where sigils is empty or k is 0.