decayedbridges

decayedbridges

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 ≤ i ≤ M), find the inconvenience just after the i-th bridge collapses.

Constraints

• All values in input are integers.
• 2 ≤ N ≤ 10⁵
• 1 ≤ M ≤ 10⁵
• 1 ≤ A_i < B_i ≤ 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
A1 B1
A2 B2
:
AM BM

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.

Sample Input 1

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

Sample Output 1

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).

Sample Input 2

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

Sample Output 2

8
9
12
14
15

Sample Input 3

2 1
1 2

Sample Output 3

1