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E. Trips
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

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 $$$i$$$.

Examples
Input
4 4 2
2 3
1 2
1 3
1 4
Output
0
0
3
3
Input
5 8 2
2 1
4 2
5 4
5 2
4 3
5 1
4 1
3 2
Output
0
0
0
3
3
4
4
5
Input
5 7 2
1 5
3 2
2 5
3 4
1 2
5 3
1 3
Output
0
0
0
0
3
4
4
Note

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 $$$7$$$.