Trips
Description
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 $i$.
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 $i$.
Samples
4 4 2
2 3
1 2
1 3
1 4
0
0
3
3
5 8 2
2 1
4 2
5 4
5 2
4 3
5 1
4 1
3 2
0
0
0
3
3
4
4
5
5 7 2
1 5
3 2
2 5
3 4
1 2
5 3
1 3
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 $7$.