Riva

Ljubo is a local strongman in a small seaside town, and tourism is his responsibility. He knows that nothing draws visitors like a walk along a well paved seafront, so he decided to fence off part of the shore and pour concrete inside it. To please the visitors as much as possible, Ljubo wants to concrete an area that is as large as possible.

The shoreline is given as a polyline that does not intersect itself. The polyline joins the vertices $(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)$ in this order and it always runs from left to right, so $x_1 < x_2 < \dots < x_N$. The sea is above the polyline and the shore is below it.

Ljubo has a rope $L$ meters long. He picks two vertices of the polyline and drives a stick into each of them. Then he stretches the rope, or only a part of the rope, between the two sticks so that it is taut. The segment spanned by the rope must not cross the sea, but it is allowed to touch the shoreline. Once the rope is in place, Ljubo pours concrete over the part of the shore that lies between the rope and the sea.

The figure matches the third example input. The black polyline is the shoreline and the grey region is the sea. Ljubo's taut rope is the grey segment, and the part of the shore that gets concrete is shaded.

Given the shoreline and the length of the rope, write a program that computes the largest area Ljubo can fence off and concrete. That area can be zero.

The first line contains the integers $N$ and $L$ ($3 \le N \le 5\,000$, $0 \le L \le 1\,000\,000$). $N$ is the number of vertices of the polyline describing the shoreline, and $L$ is the length of Ljubo's rope.

Each of the next $N$ lines contains two integers $x_i$ and $y_i$ separated by a space ($0 \le x_i, y_i \le 1\,000\,000$), the coordinates of a vertex of the shoreline. The coordinates satisfy $x_1 < x_2 < \dots < x_N$.

Print one line with the largest area Ljubo can fence off and concrete. Print it with exactly one digit after the decimal point. You may assume the area is always an integer or half an integer.