BABA1 - ARE YOU GOOD IN MATHS?


BABA taught properties of right angled triangle and asked a questions 

"Can you find a right angled triangle whose length of hypotenuse is H and its area is A?"

INDIAN students can answer quickly. 


Input

The first line of the input contains a single integer T  (where 1≤T≤10^5)  denoting the number of test-cases. T test cases follow.

For each test case, there will be a single line containing two space separated integer H and A (where 1 ≤ H ≤ 10^6  and 1 ≤ A ≤ 10^12 ).

Output

Output the answer for each test-case in a single line. If it is not possible to find such a triangle, output -1.

Otherwise print 3 real numbers corresponding to the lengths of the sides of the triangle sorted in non-decreasing order. 

NOTE:- Answer values upto 10^-6 decimal places.

Example

Input:
4
4252 56578987908
1 1
4
24252 56578987908
1 1
2 2
10 10                                                              
10 1
Output:
-1
-1
-1
2.043096 9.789063 10.000000

hide comments
prachij: 2019-08-23 08:38:48

Last edit: 2019-08-23 08:39:11
sandilya1599: 2019-07-09 09:41:22


jmr99: 2018-06-20 09:21:07

simple math ..but take,sf,pf & print double i got 3 WA !! then AC

shubham9261: 2017-10-01 23:49:20

yup,no binary search required

matcha1998: 2017-09-13 10:43:29

No Binary Search required!!
Simple geometry!!

mahilewets: 2017-08-26 11:58:16

You can solve it without binary search

But to do it you should exploit some much more complex ideas

I can't prove why formula for finding roots of square equation is correct

But I can prove that you can find root of square equation using numerical calculations

varun6325: 2017-08-23 21:11:04

Use printf instead of cout to print the double output

sagnik_66: 2017-05-28 08:59:29

Binary Search Tag is misleading! Not required at all

abhaypandey: 2017-02-20 01:59:44


Last edit: 2017-02-20 02:01:24
quantic: 2017-02-15 10:17:40

kindergarten mathematics...

Last edit: 2017-02-15 17:30:32

Added by:junior_g
Date:2017-02-14
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ADA95 ASM32-GCC ASM32 ASM64 BASH BC BF COBOL COFFEE D-CLANG D-DMD D DART ELIXIR ERL FANTOM FORTH FORTRAN CHICKEN