Magic

There are $n$ clones of Little P on the plane. The area occupied by a group of clones is the area of the smallest convex polygon that covers the group. Little P has limited abilities, so some clones disappear at each moment. Before the next moment, Little P uses a magic technique to make the disappeared clones reappear at their original positions.

Given $m$ queries, find the area occupied by the remaining clones after each moment when clones disappear.

The first line contains two positive integers $n$ and $m$, the number of clones at the beginning and the total number of queries.

The next $n$ lines contain two integers $x_i$ and $y_i$ each, the position of the $i$-th clone.

Each of the next $m$ lines starts with an integer $k$, meaning $k$ clones disappear at this moment. It is followed by $k$ non-negative integers $c_1, c_2, \ldots, c_k$, which are used to generate the numbers of the disappeared clones.

Let $S$ be twice the area occupied by the remaining clones at the previous moment. The numbers of the clones that disappear at this moment are $p_i = ((S + c_i) \bmod n) + 1$. At the first moment, take $S = -1$, so $p_i = ((-1 + c_i) \bmod n) + 1$.

For each of the $m$ moments, in the given order, print one integer on its own line: twice the area occupied by the clones that remain at that moment.

• $n \leq 10^5$
• $m \leq 10^5$
• $k \leq 100$
• $|x_i|, |y_i| \leq 10^8$
• No two clones have the same coordinates.
• The sum of $k$ over all moments does not exceed $2 \times 10^6$.
• $0 \leq c_i \leq 2^{31} - 1$
• Initially, all $n$ clones occupy an area greater than $0$.
• The set of vertices that define the region occupied by all $n$ clones is $S$, with $|S| \geq 3$. At any moment, at least two clones in $S$ have not disappeared.