# 4200. Hamster flight

## Problem code: HAMSTER1

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
```

 Added by: Spooky Date: 2009-04-10 Time limit: 2s Source limit: 50000B Memory limit: 256MB Cluster: Pyramid (Intel Pentium III 733 MHz) Languages: All except: ERL JS NODEJS PERL 6 Resource: Advancement Spring 2009, http://sevolymp.uuuq.com/

2012-10-25 19:12:23 Ashish Lavania
Spooky : my program works for all values still WA please check 7927933

Last edit: 2012-10-25 22:43:42
2012-09-26 09:14:26 Ashwin Vedachalam
@ Spooky my program gives the same junk value in my system for all d inputs but it got AC in the judge.
2012-06-24 08:09:56 DaRksTar
double wrks....:)
2012-06-04 23:23:15 15972125841321
plz tell me where i m wrog my sub id is 7091407 i m getting correct ans for test cases....
2012-02-20 19:55:51 Benjamin Pinaya
Does anybody has some more useful test cases? :D please!
2012-01-06 18:24:08 saket diwakar
finally got AC...those who r getting WA in C,take long double and pi= (3.141592653589793)..
2011-05-07 15:41:14 Gaurav