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 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

D. Follow Traffic Rules

time limit per test

1 secondmemory limit per test

64 megabytesinput

standard inputoutput

standard outputEverybody knows that the capital of Berland is connected to Bercouver (the Olympic capital) by a direct road. To improve the road's traffic capacity, there was placed just one traffic sign, limiting the maximum speed. Traffic signs in Berland are a bit peculiar, because they limit the speed only at that point on the road where they are placed. Right after passing the sign it is allowed to drive at any speed.

It is known that the car of an average Berland citizen has the acceleration (deceleration) speed of *a* km/h^{2}, and has maximum speed of *v* km/h. The road has the length of *l* km, and the speed sign, limiting the speed to *w* km/h, is placed *d* km (1 ≤ *d* < *l*) away from the capital of Berland. The car has a zero speed at the beginning of the journey. Find the minimum time that an average Berland citizen will need to get from the capital to Bercouver, if he drives at the optimal speed.

The car can enter Bercouver at any speed.

Input

The first line of the input file contains two integer numbers *a* and *v* (1 ≤ *a*, *v* ≤ 10000). The second line contains three integer numbers *l*, *d* and *w* (2 ≤ *l* ≤ 10000; 1 ≤ *d* < *l*; 1 ≤ *w* ≤ 10000).

Output

Print the answer with at least five digits after the decimal point.

Examples

Input

1 1

2 1 3

Output

2.500000000000

Input

5 70

200 170 40

Output

8.965874696353

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 10:52:51 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|