### ** 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 ≤ 10`^{5}
`1 ≤ M ≤ 10`^{5}
`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`
`A`_{1} `B`_{1}
`A`_{2} `B`_{2}
:
`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.

### 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