CF1728G Illumination

Consider a segment $ [0, d] $ of the coordinate line. There are $ n $ lanterns and $ m $ points of interest in this segment. For each lantern, you can choose its power — an integer between $ 0 $ and $ d $ (inclusive). A lantern with coordinate $ x $ illuminates the point of interest with coordinate $ y $ if $ |x - y| $ is less than or equal to the power of the lantern. A way to choose the power values for all lanterns is considered valid if every point of interest is illuminated by at least one lantern. You have to process $ q $ queries. Each query is represented by one integer $ f_i $ . To answer the $ i $ -th query, you have to: - add a lantern on coordinate $ f_i $ ; - calculate the number of valid ways to assign power values to all lanterns, and print it modulo $ 998244353 $ ; - remove the lantern you just added.

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