I. Wrong Sort of Bees
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Trying to get some honey from the top of large oak-tree, Pooh was holding a balloon in his paws and singing a song:

How sweet to be a Cloud Floating in the Blue! Every little cloud Always sings aloud.

How sweet to be a Cloud Floating in the Blue! It makes him very proud To be a little cloud.

There was a wind to blow him nearer to the tree, and Pooh moved along a straight line with constant height and constant speed $$$V_{Pooh}$$$ meters per minute. Unfortunately, direction wasn't accurate enough and he missed the tree.

Pooh suddenly noticed a bee directly at distance $$$R$$$ meters in front of him in the direction of his movement. It then began to fly around him, also maintaining the same height as Pooh. Pooh noticed (from his point of view) that the bee moves in a Definitely Suspicious way. It flies around him with constant angular velocity $$$\Omega_{bee}$$$ revolutions per minute. Furthermore, the distance between the bee and the Bear is reducing as fast as $$$V_{bee}$$$ meters per minute!

Pooh had just been thinking and faced a very important problem when the bee touched him. How long was the trajectory of the bee? It's so important because Pooh knows that a bee cannot fly too far, and if it flies too far indeed, then it belongs to the wrong sort of bees that make the wrong sort of honey in which Pooh isn't interested at all.

For the purpose of this problem, the sizes of Pooh and the bee are negligible.

Input

The first line contains the only integer $$$T$$$ ($$$1 \leq T \leq 100$$$) — number of test cases.

Each test case is a single line that contains four integers: $$$R$$$, $$$V_{Pooh}$$$, $$$V_{bee}$$$, $$$\Omega_{bee}$$$. It is guaranteed that $$$1 \leq R, V_{Pooh}, V_{bee}, \Omega_{bee} \leq 100$$$.

Output

Output $$$T$$$ lines each of which contains an answer for the corresponding test case — the length of the bee's trajectory. Numbers should be given with absolute or relative error of at most $$$10^{-4}$$$.

Example
Input
1
1 1 1 1
Output
3.367571733