2972 -- Laser-Ball

Mr. X and his friends are great funs of Laser-Ball Game. Basically, the main idea of the game is very simple. Each player of the game has a laser gun and it is necessary to hit an opponent with a laser beam. To make the game more interesting, Mr. X with friends created their own Laser-Ball playground. They rented an empty rectangular hall and set up a number of big mirrors. What makes the game more interesting is the additional ability to shoot into a mirror since that a reflected laser beam also can hit an opponent.

You need to write a program which determines if it is possible to hit an opponent standing in a point B from point A. If such a hit is possible the program needs to give a direction.

To clarify the problem the following rules are given.

There are N mirrors in the hall.
Each mirror is a rectangle. It is standing vertically on one of its edges. Therefore, a mirror can be described by a pair of coordinates (X₁, Y₁) – (X₂, Y₂), where (X₁, Y₁) ≠ (X₂, Y₂) and X_i, Y_i are real numbers. The height of a mirror is not essential for this problem.
Mirrors neither touch nor cross each other.
Both sides of a mirror have a reflection layer. A mirror reflects a laser beam according to physical laws. Let’s assume that an edge reflects in the same way as the inner part of a mirror.
Let’s assume that a mirror is absolutely thin. Thus, a laser beam can pass parallel to the mirror as close as necessary, even at 0 distance (see example 2 below)
A laser beam hits an opponent if it passes the opponent not farther then 10⁻⁴
A laser beam goes out of point A(0, 0)
A opponent is in the point B(X_B, Y_B)
A direction of a shoot, which your program needs to calculate, is a vector in a form (dx, dy)
When a laser beam hits a mirror it loses some part of its energy. After the beam hit mirrors (K+1) times it can’t hit an opponent. Any mirror can be hit more than once.
0 ≤ N ≤ 100, 1 ≤ K ≤ 10, but N^K ≤ 10⁶