URI Online Judge | 1549

Splitting the Coke

By Ricardo Oliveira, UFPR BR Brazil

Timelimit: 1

A group of N friends went to a restaurant to have lunch. Although each person decided to order a different dish, they all decided to drink Coke. The group ordered a Coke bottle with L ml, and must now split the content of the bottle between the N people in such a way that each person gets the same amount of the drink.

For each person, there is an empty cup which must be filled with the drink that person will receive. All N cups are equal, and can be described as cone frustum whose height is H cm, the smaller base has a radius equal to b cm, and the larger base has a radius equal to B cm, as indicated by the figure.


Cups filled with Coke up to the height h cm

Your task is to help the group to split the Coke bottle. You must find the height h such that, if each cup is filled with Coke up to the height h cm, then each person gets the same amount of the drink. You may assume that no cup will needed to be filled more than its capacity.

Input

The first line of input contains an integer C that determines the number of test cases. Each test case starts with a line containing two integers, N and L (1 ≤ N ≤ 100, 1 ≤ L ≤ 108), the number of friends in the group and the amount of Coke in the bottle, in milliliters. The second line contains three integers bB and H (1 ≤ bB ≤ 100, 1 ≤ H ≤ 100), the radii of the smaller and the larger base, and the height of the cups, in centimeters.

Output

For each test case, print the value of h such that all cups must be filled up to the height h cm. Print the answer with 2 decimal places.

Sample Input Sample Output

2

1 200
5 6 8
2 350
3 3 16

2.40
6.19