Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Traffic Lights

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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?

Input

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.

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 than 10^{ - 6}.

Examples

Input

2 1 3 4 5

Output

0.66666667

Input

5 4 3 1 1

Output

2.33333333

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/20/2019 05:01:05 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|