decayedbridges
Problem Statement
There are N islands and M bridges.
The i-th bridge connects the Ai-th and Bi-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 ≤ Ai < Bi ≤ N
- All pairs (Ai, Bi) 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