E. Tripstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputPrint 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.ExamplesInput4 4 22 31 21 31 4Output0033Input5 8 22 14 25 45 24 35 14 13 2Output00033445Input5 7 21 53 22 53 41 25 31 3Output0000344NoteIn 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. 
Input4 4 22 31 21 31 4
Output0033
['graphs', '*2200']