The Return of Superman

Does everyone know who Superman is? In case you don't — he's a man from another galaxy whom you can't hit with a fist, and even bullets don't work on him. In short, he's almost invincible. However, there is a substance that has a deadly effect on him — pieces of green meteorite from his home planet. When they're nearby, Superman loses his extraordinary abilities.

Cunning enemies of Superman have wounded him with a bullet made of green meteorite. Now he is slowly dying. His only salvation is to reach the Fortress, his only connection to his home planet. There, the bullet will be removed and he will recover.

Let's consider this problem on a plane. Superman was wounded at the point S(x_1, y_1). The Fortress is located at the point F(x_2, y_2). Superman's initial speed is $V$ m/s. Each second, due to his wound, it decreases by $A$ units. Furthermore, each meter traveled further reduces his speed by $B$ units. These decreases happen continuously. If his speed drops to zero, Superman can no longer move.

As if that weren't enough, somewhere nearby there are deposits of the same green meteorite (considered as a point). Depending on the amount of substance, they have a radius of effect. The radius of effect refers to the radius of a circular area within which the influence of the substance is spread. If the wounded Superman finds himself inside this area, he will die.

You are given x_1, y_1, x_2, y_2 — the initial coordinates of Superman and the Fortress. You are also given $X$, $Y$, $R$ — the coordinates of the meteorite deposit and its radius of effect. Finally, you are given $V$, $A$, and $B$.

If Superman cannot reach the Fortress, output -1 (without quotes). Otherwise, output the minimum time in which he can do it.

It is guaranteed that if Superman cannot reach the Fortress, he will stop at least $0.000001$ (1 \times 10^{-6}) away from the Fortress.