Problem Statement

There are $N$ islands and $M$ bridges connecting them. Bridge $i\ (1\leq i\leq M)$ connects islands $U_i,V_i$.
Initially, some of the islands are connected to each other by these $M$ bridges.

However, due to large-scale crustal movements, these bridges collapse at a rate of $1$ bridge every $1$ day.
You are given a collapse schedule spanning $Q$ days. On day $i$ $(1\leq i\leq Q)$, bridge $B_i$ collapses and becomes impassable.

As the country's Minister of Transport, you must report at the end of each day the total number of pairs of islands that cannot reach each other.
For each day $i=1,2,\dots,Q$, compute the total number of pairs of islands that cannot reach each other after that day's bridge collapse.

Formally, for each day $i$ $(1\leq i\leq Q)$, find the following value after that day's bridge collapse.

• The number of pairs of integers $(i,j)$ satisfying $1\leq i<j\leq N$ such that islands $i$ and $j$ cannot reach each other no matter how many bridges are used

Input

$N\ M$
$U_1\ V_1$
$\dots$
$U_M\ V_M$
$Q$
$B_1$
$\dots$
$B_Q$

• $2\leq N\leq 2\times 10^5$
• $1\leq M\leq 2\times 10^5$
• $1\leq U_i,V_i\leq N\ (1\leq i\leq M)$
• $U_i\neq V_i\ (1\leq i\leq M)$
• $1\leq Q\leq M$
• $1\leq B_i\leq M\ (1\leq i\leq Q)$
• $B_i\neq B_j\ (1\leq i,j\leq Q,i\neq j)$

Output

Output $Q$ lines, separated by newlines, giving the total number of pairs of islands that cannot reach each other at the end of each day.
Print a newline at the end.

Sample

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

0
0
4

3 2
1 2
1 2
2
2
1

2
3