Equally-spaced parallel lines lie on an infinite plane. The separation between adjacent lines is D (D>0). Now considering a circle of diameter D. N points lie on or in the circle. It is guaranteed that any three points are not collinear. Between any two points there's a needle. Find the possibility that, if the circle is randomly (with equal probability on any position and direction) thrown onto the same plane described above (with the equally-spaced parallel lines of separation d), at least one needle crosses a line.
The first line contains a single integer T (1 <= T <= 100), the number of test cases.
For each set of input data, the first line gives two integers, N and D (N<=100), as described above.
You can consider the center of the circle is default as the origin. Lastly N lines is followed, each containing two real numbers that representing the coordinate of a point lying within the circle.
Each output should occupy one line. Each line should start with "Case #i: ", followed by a real number round to four decimal places, the probability that at least one needle crosses one line.