Determine the Price

Time limit: 1 Seconds

Memory limit: 32768K

For the manager of a theatre, setting the price of a ticket is a rather delicate matter. Suppose that a theatre has n (<= 1000000) seats, and that if you give away the tickets for free, all the seats will be taken. After some sort of investigation, it is estimated that for every p yuans of increase of the ticket price, the theatre will lose m audiences. But the audiences will not leave until the ticket price jumps up a complete step of p yuans. For example, if given p=1.00 and m=10, no audience will be lost if the price is set to be 0.99 yuans, and 10 will be lost if the price is 1.99 yuans. It costs R yuans for the theatre to run each show, and S yuans to serve each of the audiences during each show. Now your job is to write a program to maximize the total revenue of each show for the theatre.

1. Input

The first line of input contains a positive integer N (< 10000), then followed by N test cases.

Each test case consists of 5 positive numbers in a line, n, p, m, R, S which are all defined in the problem.

2. Output

For each test case, print the optimal price of a ticket, the total number of audiences to sit in the theatre with that price set, and the maximum revenue, in the format illustrated by the sample output.

Note: the unit of price is RMB yuan, and a price must be rounded off to 2 decimal places. There must be one blank line between two test cases, but no extra line at the end of output.

3. Sample Input

1000 0.10 10 1000 2.00
100 0.50 2 500 2.0

4. Sample Output

price = 6.09
audiences = 400
revenue = 636.00

price = 13.99
audiences = 46
revenue = 51.54

Problem Source: Zhejiang University Local Contest 2002

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