B"Imagine a board with n pins put into it, the i -th pin is located at (x_i, y_i) . For simplicity, we will restrict the problem to the case where the pins are placed in vertices of a convex polygon. Then, take a non-stretchable string of length l , and put it around all the pins. Place a pencil inside the string and draw a curve around the pins, trying to pull the string in every possible direction. The picture below shows an example of a string tied around the pins and pulled by a pencil (a point P ). Your task is to find an area inside this curve. Formally, for a given convex polygon S and a length l let's define a fiber shape F(S, l) as a set of points t such that the perimeter of the convex hull of S cup {t } does not exceed l . Find an area of F(S, l) . The first line contains two integers n and l ( 3 <= n <= 10^4 ; 1 <= l <= 8 cdot 10^5 ) -- the number of vertices of the polygon S and the length of the string. Next n lines contain integers x_i and y_i ( -10^5 <= x_i, y_i <= 10^5 ) -- coordinates of polygon's vertices in counterclockwise order. All internal angles of the polygon are strictly less than pi . The length l exceeds the perimeter of the polygon by at least 10^{-3} . Output a single floating-point number -- the area of the fiber shape F(S, l) . Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6} . The following pictures illustrate the example tests. "...