CF29B.Traffic Lights

A car moves from point A to point B at speed v meters per second. The action takes place on the X-axis. At the distance d meters from A there are traffic lights. Starting from time 0, for the first g seconds the green light is on, then for the following r seconds the red light is on, then again the green light is on for the g seconds, and so on.

The car can be instantly accelerated from 0 to v and vice versa, can instantly slow down from the v to 0. Consider that it passes the traffic lights at the green light instantly. If the car approaches the traffic lights at the moment when the red light has just turned on, it doesn't have time to pass it. But if it approaches the traffic lights at the moment when the green light has just turned on, it can move. The car leaves point A at the time 0.

What is the minimum time for the car to get from point A to point B without breaking the traffic rules?

一辆汽车以 $v$ 米/秒的速度从点 A 向点 B 行驶。整个过程发生在 X 轴上。在距 A 点 $d$ 米处设有交通信号灯。从时刻 0 开始，绿灯持续亮 $g$ 秒，随后红灯持续亮 $r$ 秒，接着再次绿灯亮 $g$ 秒，如此循环往复。

汽车可瞬间从静止加速至速度 $v$，也可瞬间从速度 $v$ 减速至静止。假设汽车恰在绿灯亮起时通过交通信号灯，则视为瞬时通过；若汽车抵达交通信号灯时恰好红灯刚亮起，则无法通过；但若汽车抵达交通信号灯时恰好绿灯刚亮起，则允许通行。汽车于时刻 0 从点 A 出发。

在不违反交通规则的前提下，汽车从点 A 到达点 B 所需的最短时间是多少？

The first line contains integers l, d, v, g, r (1 ≤ l, d, v, g, r ≤ 1000, d < l) — the distance between A and B (in meters), the distance from A to the traffic lights, car's speed, the duration of green light and the duration of red light.

第一行包含整数 $l$、$d$、$v$、$g$、$r$（$1 ≤ l, d, v, g, r ≤ 1000$，且 $d < l$）—— 分别表示 A 与 B 之间的距离（单位：米）、A 到交通灯的距离、汽车的速度、绿灯持续时间以及红灯持续时间。

Output a single number — the minimum time that the car needs to get from point A to point B. Your output must have relative or absolute error less than 10 - 6.

输出一个数字——汽车从点 A 到点 B 所需的最短时间。你的输出结果的相对误差或绝对误差必须小于 $10^{-6}$。