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D - Decayed Bridges

Score : $400$ points

Problem Statement

There are $N$ islands and $M$ bridges.

The $i$-th bridge connects the $A_i$-th and $B_i$-th islands bidirectionally.

Initially, we can travel between any two islands using some of these bridges.

However, the results of a survey show that these bridges will all collapse because of aging, in the order from the first bridge to the $M$-th bridge.

Let the inconvenience be the number of pairs of islands $(a, b)$ ($a < b$) such that we are no longer able to travel between the $a$-th and $b$-th islands using some of the bridges remaining.

For each $i$ $(1 \leq i \leq M)$, find the inconvenience just after the $i$-th bridge collapses.

Constraints

• All values in input are integers.
• $2 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• $1 \leq A_i < B_i \leq N$
• All pairs $(A_i, B_i)$ are distinct.
• The inconvenience is initially $0$.

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

In the order $i = 1, 2, ..., M$, print the inconvenience just after the $i$-th bridge collapses. Note that the answer may not fit into a $32$-bit integer type.

4 5
1 2
3 4
1 3
2 3
1 4

0
0
4
5
6

For example, when the first to third bridges have collapsed, the inconvenience is $4$ since we can no longer travel between the pairs $(1, 2), (1, 3), (2, 4)$ and $(3, 4)$.

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

8
9
12
14
15

2 1
1 2

1