Traffic Lights

A car moves from point A to point B at speedvmeters per second. The action takes place on the X-axis. At the distancedmeters from A there are traffic lights. Starting from time 0, for the firstgseconds the green light is on, then for the followingrseconds the red light is on, then again the green light is on for thegseconds, and so on.

The car can be instantly accelerated from0tovand vice versa, can instantly slow down from thevto0. 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?

Input

The first line contains integersl,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.

Output

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 than10 - 6.

Examples

input

Copy

2 1 3 4 5

output

Copy

0.66666667

input

Copy

5 4 3 1 1

output

Copy

2.33333333

翻译：

‎汽车以每秒 ‎‎v‎‎ 米的速度从 A 点移动到 B 点。该操作在 X 轴上发生。在距离A‎‎的d‎‎米处有红绿灯。从时间 0 开始，在前 ‎‎g‎‎ 秒内，绿灯亮起，然后在接下来的 ‎‎r‎‎ 秒内红灯亮起，然后绿灯再次亮‎‎起 g‎‎ 秒，依此类推。‎

‎汽车可以从‎‎0‎‎到‎‎v‎‎立即加速，反之亦然，可以从‎‎v‎‎立即减速到‎‎0‎‎。考虑到它立即通过绿灯处的交通信号灯。如果汽车在红灯刚刚亮起的那一刻接近红绿灯，它没有时间通过它。但是，如果它在绿灯刚刚打开的那一刻接近交通信号灯，它可以移动。汽车在 0 时离开点 A。‎

‎在不违反交通规则的情况下，汽车从A点到B点的最短时间是多少？‎

‎输入‎

‎第一行包含整数 ‎‎l‎‎， ‎‎d‎‎， ‎‎v‎‎， ‎‎g‎‎， ‎‎r‎‎ （‎‎1 ≤ ‎‎l‎‎， ‎‎d‎‎， ‎‎v‎‎， ‎‎g‎‎,‎‎r‎‎ ≤ 1000， ‎‎d‎‎ < ‎‎l‎‎)A 和 B 之间的距离（以米为单位）、从 A 到红绿灯的距离、车速、绿灯持续时间和红灯持续时间。‎

‎输出‎

‎输出单个数字 — 汽车从 A 点到 B 点所需的最短时间。输出的相对或绝对误差必须小于‎10‎^-6

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