KPGAME - A game with probability

Alice and Bob play the following game. First, they collect N small stones and put them together in one pile. After that, they throw a coin one by one. Alice starts first. If a player throws heads then he takes exactly one stone from the pile. In case of tails he don't do anything. The one who takes the last stone wins. For each player, his skill of throwing a coin is known (to everyone, including himself and his opponent). More precisely, if Alice wants to throw some specific side of the coin, she always succeeds with probability P. The same probability for Bob is Q. You are to find probability that Alice will win the game if both guys play optimally.

Input

Input starts with a line containing one integer T - a number of test cases (1 <= T <= 50). Then T test cases follow. Each of them is one line with three numbers N, P, and Q separated with a space (1 <= N <= 99999999, 0.5 <= P, Q <= 0.99999999). P and Q have not more than 8 digits after decimal point.

Output

For each test case output one line with a probability that Alice will win the game. Your answer must be precise up to 10^-6.

Example

Input:
1
1 0.5 0.5

Output:
0.666666667

Added by:Pavel Kuznetsov
Date:2009-03-16
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Vologda 2009

hide comments
2015-06-04 14:55:23 Mayank Poply
can anyone give some more test cases?
plzz
2011-07-26 19:00:36 Efim
I enjoyed it.
2011-05-24 03:52:01 Martin
How to AC this problem in JAVA? I always gets "runtime error" with "(NZEC)".
I think there must be something wrong in the input data.

Last edit: 2011-05-24 03:52:47
2009-08-20 03:25:57 ~ adieus ~
a total maths problem.

Last edit: 2009-08-20 03:27:09
2009-03-16 19:40:26 Pavel Kuznetsov
If X is your answer and Y author's answer, then you'll get accepted only if |X-Y|<=10^-6. So, if the correct answer is 0.123 then you can just output 0.123 or 0.122999999999999999.
2009-03-16 17:11:15 .:: Pratik ::.
how many digits to print in decimal ?
The output is not clear to me
It says : "Your answer must be precise up to 10^-6"
But sample output has 9 digits.
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