REBOUND  The return of the Cake
It is well known that, in byteland, when you throw a cake, the angle of reflexion is not the angle of incidence. Measured from the ground, the angle is the double, in byteland!
You stand at point A(0, z), and you want to throw a cake in Leo's face. Leo stands at B(x, y) and is a very dangerous man, so you decide to use the ground in order to make your cake rebound.
Your shot is precise only if you can use an integer value t in the intervall [0, x], in order to reflect on C(t, 0). Sometimes it's possible, sometimes not!
Input
The input begins with the number T of test cases in a single line. In each of the next T lines there are three integers x, y and z, explaining the locations : you A(0, z), Leo B(x, y).
Output
For each test case, find and print the only integer t such 0 <= t <= x, that allow this perfect shot. If it's not possible, output "Not this time.".
Example
Input: 3 5 4 1 6 5 2 7 3 1 Output: 2 Not this time. 3
Comment : the last case is the one illustrated above.
Constraints
1 < T < 100 000 0 < x < 1 000 000 000 0 < y < 1 000 000 000 0 < z < 1 000 000 000
Edit(20170211) : New time limit (after compiler changes).
hide comments
sonuverma:
20180202 16:29:02
Nice Problem :) 

cs_abhi2000:
20170111 08:08:12
@Mayank Pratap Thank u for giving hint... 

alok singh:
20150824 09:50:10
clang rocks... green in one go @shantanu tripathi :p 

[Mayank Pratap]:
20150619 10:41:44
Try to avoid overflow... Nice problem on algebra and trigo ... 

Naman Goyal:
20150520 04:28:33
This is weird, I didn't know that C++ (4.3.2) sqrt function has some problems with unsigned long long int. Costed me like infinite WA's . Finally just removing unsigned worked and got AC. 

Harshit:
20150328 19:11:39
any typical test case??


pika_pika:
20130716 20:03:45
easy but the damned '.' cause so many WA's


sam:
20130217 14:32:11
please give me some more tricky test cases


sam:
20130215 17:49:12
what is output for x=0,y=0,z=0..........................

Added by:  Francky 
Date:  20120526 
Time limit:  0.75s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own problem 