Solar rocket P64151

At a planet far away, an alien civilization is developing a rocket that works with solar energy. Assume this simplified model: The rocket is a point that moves vertically. Due to gravity, there is a constant downward acceleration of $a$ everywhere. At the rocket location, there are $h$ hours of daytime, followed by $h$ hours of nighttime, followed by $h$ hours of daytime, etc. During the daytime hours, the solar engines of the rocket provide an upward acceleration of $b$. Will the rocket reach a vertical distance of $d\,$? If so, can you compute the first time to reach that point?

Input

Input consists of several cases, each with $a$, $b$, $h$ and $d$. Assume that $a$ and $b$ are real numbers such that $1 \le a < b \le 10$, that $h$ is an integer number between 1 and 20, that $d$ is an integer number between 1 and 10000, and that all the units used are km and hours.

Output

For every case, print “never” if the rocket will never reach height $d$. Otherwise, print the minimum time to reach that height, with four digits after the decimal point. The input cases have no precision issues, nor ill-conditioned cases. With the given cases, the answer will never be larger that 200 hours.