CF985E Pencils and Boxes

Mishka received a gift of multicolored pencils for his birthday! Unfortunately he lives in a monochrome world, where everything is of the same color and only saturation differs. This pack can be represented as a sequence $ a_{1},a_{2},...,a_{n} $ of $ n $ integer numbers — saturation of the color of each pencil. Now Mishka wants to put all the mess in the pack in order. He has an infinite number of empty boxes to do this. He would like to fill some boxes in such a way that: - Each pencil belongs to exactly one box; - Each non-empty box has at least $ k $ pencils in it; - If pencils $ i $ and $ j $ belong to the same box, then $ |a_{i}-a_{j}|

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In the first example it is possible to distribute pencils into $ 2 $ boxes with $ 3 $ pencils in each with any distribution. And you also can put all the pencils into the same box, difference of any pair in it won't exceed $ 10 $ . In the second example you can split pencils of saturations $ [4,5,3,4] $ into $ 2 $ boxes of size $ 2 $ and put the remaining ones into another box.