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 $7$ .