Divisibility and Game Strategy in Array Modification Problems

Problem A: Interval Coverage with Exclusions Given a sequence of operations on an integer range [p, q] (initially [1, 10^9]), each operation falls into one of three types: Type 1: increase the lower bound to max(current lower bound, k) Type 2: decrease the upper bound to min(current upper bound, k) Type 3: add value k to a list of excluded poin ...

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