HAMSTER1 - Hamster flight


There is a competition of flying hamsters in Hamsterburg. Each competing hamster is thrown from a sling. The judges rate the flight according to its length and height. Let X meters be the distance of the flight, and Y meters – maximum height to which the hamster rose during the flight. The hamster will receive K1*X + K2*Y points for such a flight. The initial speed of the hamsters is V0 m/s. Free fall acceleration is g = 10 m/s2. There is no air friction. The size of the hamster and the sling are negligible. When the hamster is thrown from the sling its height is 0 meters. You should determine the angle at which the hamster must be thrown so that he receives maximum points.

Input

The first line of input contains number t – the amount of tests. Then t tests follow one per line. The description of each test consists of three integers separated by single spaces. The first integer is V0, the second – K1, the third – K2.

Constraints

1 <= t <= 10000
1 <= V0 <= 100
0 <= K1, K2 <= 1000
0 < K1 + K2

Output

For each test output the angle in radians at which the hamster must be thrown, and the amount of points it will receive. The numbers should be separated with spaces. Print the numbers with exactly three digits in the fractional part.

Example

Input:
3
10 10 0
10 0 10
10 10 10

Output:
0.785 100.000
1.571 50.000
0.908 128.078

hide comments
marethyu1: 2018-12-29 21:18:06

In order to use binary search, I believe it's same idea as finding a peak element in an array.

Kuba S: 2018-10-30 16:52:31

Ternary search + double prec. got me AC in cpp.
Plotting height and distance functions will help you understand the search space.
More on ternary search: https://en.wikipedia.org/wiki/Ternary_search

shimul07: 2018-09-20 14:42:25

How to get theta ? Can anybody explain,plz?

pradeep_yadav: 2017-09-02 12:34:14

basic calculus would do :)

sxie12: 2017-07-10 06:37:16

Solved with ternary search on the assumption that the objective function is unimodal. Still can't figure out why that's the case though. X is unimodal and Y is monotonically increasing. The sum may be bimodal if K2 is big and K1 small. Are the constraints on K1, K2 keeping it unimodal?

viratian_070: 2017-06-28 12:34:01

high school mathematics...easy one

mishra10: 2017-06-09 10:37:52

Try to solve this problem with ternary search apart from the basic math maxima minima method..

razor123: 2017-03-06 10:07:35

search space=0 to 314159265/2 for binary search

mkfeuhrer: 2016-07-02 14:14:12

how to do with binary search.... i did simple maths n projectile ..!

Hemant Kumar Singh: 2016-05-28 20:52:27

Any hints for the binary search approach? I did by the simple equation method.


Added by:Spooky
Date:2009-04-10
Time limit:0.418s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Advancement Spring 2009, http://sevolymp.uuuq.com/