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Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

Given is an undirected graph with $N$ vertices and $M$ edges.
Edge $i$ connects Vertices $A_i$ and $B_i$.

We will erase Vertices $1, 2, \ldots, N$ one by one.
Here, erasing Vertex $i$ means deleting Vertex $i$ and all edges incident to Vertex $i$ from the graph.

For each $i=1, 2, \ldots, N$, how many connected components does the graph have when vertices up to Vertex $i$ are deleted?

Constraints

  • $1 \leq N \leq 2 \times 10^5$
  • $0 \leq M \leq \min(\frac{N(N-1)}{2} , 2 \times 10^5 )$
  • $1 \leq A_i \lt B_i \leq N$
  • $(A_i,B_i) \neq (A_j,B_j)$ if $i \neq j$.
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_M$ $B_M$

Output

Print $N$ lines.
The $i$-th line should contain the number of connected components in the graph when vertices up to Vertex $i$ are deleted.

Sample Input 1

6 7
1 2
1 4
1 5
2 4
2 3
3 5
3 6

Sample Output 1

1
2
3
2
1
0


The figure above shows the transition of the graph.

Sample Input 2

8 7
7 8
3 4
5 6
5 7
5 8
6 7
6 8

Sample Output 2

3
2
2
1
1
1
1
0

The graph may be disconnected from the beginning.