Archimedean Spiral

Dima recently joined the Research Institute of Flat Curves. As the name of this research institute implies, it is engaged in various studies in the field of plane curves. Recently, Dimin's boss George encountered a very interesting curve, which, as it turned out after some research, is known as the Archimedean spiral. The Archimedean spiral is a flat curve depicting the trajectory of point M, which moves uniformly along the OK ray with the origin in O, while the OK ray itself rotates uniformly around point O (see figure). In other words, the distance to the origin of coordinates p = OM linearly depends on the angle of rotation φ of the beam OK. In this case, the rotation of the beam OK by the same angle corresponds to the same increment of the distance p.

The motion of the point M can be set using a number of parameters:

• the initial angle of rotation α of the beam OK (measured in degrees counterclockwise relative to the positive direction of the OX axis);

• angular velocity of rotation ω of the beam OK (measured in degrees per unit of time);

• the initial distance R from point M to the origin (point O);

• the speed of movement V of the point M along the beam is OK.

If, by setting these parameters, you do not limit the time of movement of the point M, then you will get an infinite curve, which is quite difficult to explore. Therefore, Dima decided to limit himself to studying some part of this curve, the one that is obtained when the point M moves from the zero moment of time to the moment of time T. The task that Dima solves is to find a rectangle of minimal area with sides parallel to the coordinate axes in which it can be inscribed.

You need to write a program that will find the desired rectangle