Delivering Carcinogen

2000ms

262144K

Description:

Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.

You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point (0, 0). Persephone goes round Diatar along a circular orbit with radius R in the counter-clockwise direction at constant linear speed v_p (thus, for instance, a full circle around the star takes $\text{[math]}$ of time). At the initial moment of time Persephone is located at point (x_p, y_p).

At the initial moment of time Qwerty's ship is at point (x, y). Qwerty can move in any direction at speed of at most v (v > v_p). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance r (r < R) from the star.

Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.

Input:

The first line contains space-separated integers x_p, y_p and v_p ( - 10⁴ ≤ x_p, y_p ≤ 10⁴, 1 ≤ v_p < 10⁴) — Persephone's initial position and the speed at which it goes round Diatar.

The second line contains space-separated integers x, y, v and r ( - 10⁴ ≤ x, y ≤ 10⁴, 1 < v ≤ 10⁴, 1 ≤ r ≤ 10⁴) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.

It is guaranteed that r² < x² + y², r² < x_p² + y_p² and v_p < v.

Output:

Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed 10^- 6.

Sample Input:

10 0 1
-10 0 2 8

Sample Output:

9.584544103

Sample Input:

50 60 10
50 60 20 40

Sample Output:

0.000000000

Informação

Provedor Codeforces

Código CF198C