CF1037E Trips

There are $ n $ persons who initially don't know each other. On each morning, two of them, who were not friends before, become friends. We want to plan a trip for every evening of $ m $ days. On each trip, you have to select a group of people that will go on the trip. For every person, one of the following should hold: - Either this person does not go on the trip, - Or at least $ k $ of his friends also go on the trip. Note that the friendship is not transitive. That is, if $ a $ and $ b $ are friends and $ b $ and $ c $ are friends, it does not necessarily imply that $ a $ and $ c $ are friends. For each day, find the maximum number of people that can go on the trip on that day.

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In the first example, - $ 1,2,3 $ can go on day $ 3 $ and $ 4 $ . In the second example, - $ 2,4,5 $ can go on day $ 4 $ and $ 5 $ . - $ 1,2,4,5 $ can go on day $ 6 $ and $ 7 $ . - $ 1,2,3,4,5 $ can go on day $ 8 $ . In the third example, - $ 1,2,5 $ can go on day $ 5 $ . - $ 1,2,3,5 $ can go on day $ 6 $ and $ 7 $ .