Beach cut

The seashore is modeled as a polyline with no self-intersections, given by its vertices $(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)$ listed in order, whose $x$-coordinates are strictly increasing ($x_i < x_{i+1}$). The sea lies above the polyline and the beach lies below it.

You may connect two of these vertices with a single straight segment whose length is at most $L$. Choose the two vertices so that the beach area enclosed between the segment and the shore is as large as possible. The segment must never enter the sea: it may touch the shore polyline but must not cross above it.

The first line contains two integers $N$ and $L$. After that come the $N$ vertices as integer pairs $x_1\ y_1\ x_2\ y_2\ \ldots\ x_N\ y_N$ (whitespace and line breaks may separate the numbers freely).

Print the maximum beach area that can be enclosed (it may be $0$). Because every vertex has integer coordinates, this area is always an exact multiple of $\frac{1}{2}$. Print it exactly, with no rounding: as a plain integer when the area is whole, otherwise followed by a single decimal digit $.5$ (for example, $1.5$).

• $3 \le N \le 5000$
• $0 \le x_i, y_i, L \le 1000000$
• $x_i < x_{i+1}$ for every $i$