Conic Distance
A cone is located in 3D such that its base of radius r is in the z = 0 plane with the center at (0,0,0). The tip of the cone is located at (0, 0, h). Two points are given on the cone surface in conic coordinates. The conic coordinates of a point p lying on the surface of the cone are two numbers: the first, d, is the distance from the tip of the cone to p and the second, A < 360, is the angle in degrees between the plane y = 0 and the plane through points (0,0,0), (0,0,h) and p, measured counterclockwise from the direction of the x axis.
Given are two points p_1 = (d_1, A_1) and p_2 = (d_2, A_2) in the conic coordinates. What is the (shortest) distance between p_1 and p_2 measured on the surface of the cone?
Input
The input is a sequence of lines. Each line contains 6 floating point numbers giving values of: r, h, d_1, A_1, d_2, and A_2.
Output
For each line of input, output the (shortest) distance between points p_1 and p_2 on the surface of the cone with the fraction rounded to 2 decimal places.