Magic

There are $n$ clones of Little P on the plane. Define the area occupied by a group of instances as the smallest convex polygon that covers this group of instances. Little P has limited abilities, and some clones will disappear every moment. But before the next moment, Little P will use the magic technique to make these disappeared clones reappear in their original positions.

Given $m$ queries, after each moment when the clone disappears, what is the area occupied by the remaining clone?

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

The next $n$ line, the $i$ line has two integers $x_i, y_i$ , describing the position of the $i$th clone.

In the next $m$ lines, the first integer $k$ in each line indicates that $k$ clones have disappeared at this moment. Next there are $k$ non-negative integers $c_1, c_2, \ldots, c_k$, which are used to generate the numbers of the disappeared clones.

Generated as follows:

Assume twice the area occupied by the avatar at the previous moment is $S$. Then the numbers of the clones $p_1, p_2, \ldots , p_k$ that disappeared at this moment are: $p_i = [(S + c_i) \bmod n] + 1$.

In particular, at the first moment, we believe that $S = -1$ in the previous moment, that is: the numbers of the clones $p_1, p_2, \ldots , p_k$ that disappeared at the first moment are: $p_i = [(-1 + c_i) \bmod n] + 1$.

Output the $m$ lines sequentially in the order of the given time, each line is an integer, representing twice the area occupied by the remaining clones at that time.

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