Background

Rana: Tomori, listen to me.

Rana: Washing machines are so interesting.

Tomori: Huh... a washing machine...?

Rana: The clothes keep spinning around, and watching that is really fun.

Rana: Tomori can go try it too.

Tomori: Huh...? Okay...!

"Spinning around all the time is really fun!"

Problem Description

While rana and tomorin were watching the clothes in a washing machine, they found that the clothes perform uniform circular motion. They know the initial position of the clothes, the observation time, and the washing machine’s rotational speed. Please help them find the length of the displacement from the initial position to the position at the end of the observation. The clothes can be treated as a point mass.

Input Format

The input has three lines.

The first line contains two integers $x, y$ ($-1000 \leq x, y \leq 1000$), representing the coordinates of the clothes’ initial position in a 2D Cartesian coordinate system with the washing machine center as the origin. The unit is unit length.

The second line contains a real number $t$ ($0 \leq t \leq 100$), representing the observation time, in units of unit time.

The third line contains a real number $v$ ($0 \leq v \leq 100$), representing the washing machine’s rotational speed, in revolutions per unit time.

Output Format

Output only one line.

Output a real number as the answer. A solution is considered correct if the absolute error or relative error compared to the standard answer does not exceed $10^{-6}$.

-1 0
11
0.5

2.0000000000

-1 0
10
0.5

0.0000000000

Hint

Translated by ChatGPT 5