Decayed Bridges

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.

Examples

Input

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

Output

0 0 4 5 6

Input

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

Output

8 9 12 14 15

Input

2 1 1 2

Output

1

inputFormat

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

outputFormat

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.

Examples

Input

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

Output

0 0 4 5 6

Input

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

Output

8 9 12 14 15

Input

2 1 1 2

Output

1

样例

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

8
9
12
14
15

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