Anti-missile intercept

You have to write software that shoots down a missile fired by the enemy. The situation is modeled as a simple two dimensional plane. The enemy launches its missile from $(x_m, 0)$ on the $x$ axis, and you launch your anti-missile from $(x_a, 0)$. All lengths are in feet.

At the moment of launch the enemy missile has velocity $v_x$ in the $x$ direction and $v_y$ in the $y$ direction, in feet per second. The missile is launched at time $0$, so at any later time $t$ it is at

$(x_m + v_x t,\; v_y t - 16 t^2)$

The image below draws one possible pair of trajectories. The missile follows a parabola and the anti-missile follows a straight line. In this picture $v_x$ is negative. $v_y$ is always positive.

Your commanders want the missile destroyed at a specific time $t_K$. Work out when to fire your anti-missile and what launch angle $\alpha$ to use, so that it meets the missile at exactly that time. You are also given $v_a$, the speed of your anti-missile along its straight trajectory.

Sometimes the missile cannot be destroyed at time $t_K$. It cannot be destroyed if either of the following holds.

• You would have to fire the anti-missile before time $0$, that is, the launch time $t_L$ is negative.
• The height of the missile at time $t_K$ is $0$ or less, so it has already landed and blown up.

In that case the software sounds an alarm so that everyone can start running.

One line holds six integers $x_m$, $v_x$, $v_y$, $x_a$, $v_a$, $t_K$, separated by spaces, where $0 < v_y, v_a, t_K \le 10000$, $-10000 \le x_m, v_x, x_a \le 10000$, and $x_m \ne x_a$.

If the missile cannot be destroyed at time $t_K$, print start running.

Otherwise print the launch time $t_L$ and the launch angle $\alpha$ on one line, separated by a single space. Round both values to exactly eight digits after the decimal point and print all eight digits.

$\alpha$ is in degrees, measured counterclockwise from the positive $x$ direction, and always satisfies $0 < \alpha < 180$.