Not Too Convex Hull

Nails and Rubber Bands. That is the suggestive name of a game played by a group of children (all of them offspring of geometry teachers). The children fix a number of nails on a plank of wood, at random positions. Then they choose one of the nails to be the Origin and prepare $B$ rubber bands. The challenge is to use the $B$ rubber bands to wrap the nails so that:

1. each rubber band wraps a subset of the nails;
2. every nail is inside some wrapping;
3. the wrappings do not overlap one another, except at the Origin nail, which is touched by all of the rubber bands;
4. each rubber band forms a wrapping that is a convex polygon with at least three corners;
5. the total area covered by the wrappings is the smallest among all possible ways of wrapping the nails.

An instance of the game is shown in Figure 1.

Figure 1: A game with 19 nails and 2 rubber bands

Your program must solve several instances of the game. Each game description starts with a line containing two integers $B$ and $N$, giving respectively the number of rubber bands and the number of nails, with $2 \le B \le 50$ and $2B+1 \le N \le 101$. The following $N$ lines describe the positions of the nails; each line contains two integers $X$ and $Y$ ($-10000 \le X, Y \le 10000$). The Origin is the first nail in the input. The end of input is indicated by $B = N = 0$.

In every game in the input:

• no two nails share the same point;
• no three nails lie on the same line;
• the Origin nail does not belong to the convex hull of all the nails; that is, if you use a single rubber band to wrap all the nails it never touches the Origin nail, because the Origin lies strictly inside the hull.

For each game, output a single line with the smallest total area covered by the wrappings. Print the area as a real number with two decimal places, rounding the last digit. The input contains no test cases where rounding differences are significant.