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.

The first line contains three integers $ n $ , $ m $ , and $ k $ ( $ 2 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 2 \cdot 10^5 $ , $ 1 \le k < n $ ) — the number of people, the number of days and the number of friends each person on the trip should have in the group. The $ i $ -th ( $ 1 \leq i \leq m $ ) of the next $ m $ lines contains two integers $ x $ and $ y $ ( $ 1\leq x, y\leq n $ , $ x\ne y $ ), meaning that persons $ x $ and $ y $ become friends on the morning of day $ i $ . It is guaranteed that $ x $ and $ y $ were not friends before.

Print exactly $ m $ lines, where the $ i $ -th of them ( $ 1\leq i\leq m $ ) contains the maximum number of people that can go on the trip on the evening of the day $ i $ .

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 $ .