Hard Evidence

The reporter Janne wants to photograph a secret installation to obtain decisive evidence. The installation is surrounded by a tall fence carrying high-voltage wires, so to avoid being electrocuted Janne must take the photo from outside the fence. He can raise his tripod to the height of the fence, so if he likes he may stand right up against the fence to shoot.

The installation is a convex polygon, and the fence is a circle centered at the origin. Janne wants the installation to appear as large and detailed as possible. The level of detail depends on the view angle under which the installation is seen from the chosen point, so he wants to find the point that maximizes this angle.

The photo is taken from a point on the fence, that is, from a point on the circle of radius $r$ centered at the origin. The view angle at a point is the angle between the two tangent lines drawn from that point to the polygon (equivalently, the angular width the polygon occupies as seen from the point). Report the maximum possible view angle.

The first line contains two integers $n$ and $r$ — the number of vertices of the polygon and the radius of the fence ($3 \le n \le 200$, $1 \le r \le 1000$).

Each of the next $n$ lines contains two real numbers, the coordinates of one vertex, listed in counterclockwise order. All vertices lie strictly inside the fence circle (never on its boundary), and the polygon is guaranteed to be convex. The center of the fence circle is the origin $(0, 0)$.

Print the maximum view angle $a$ (in radians, $0 \le a < 2\pi$) on a single line, rounded to exactly $10$ digits after the decimal point.