Problem
Ninjutsu is the martial art of the mysterious Japanese assassins, ninja. As a beginner in the practice of ninjutsu, your first task is to master the use of the grappling hook.
A grappling hook is a technologicallyadvanced device consisting of a hook tied to some (very strong and very thin) rope. Proper use of a grappling hook involves throwing the hook at a target and hoping that it catches.
This time, it did! You are now hooked onto a target that is located at (0,
0). Your rope extends to the left, and you're at the end of it; when you jump,
you will start swinging counterclockwise around the target. There are other
targets located to the right and above (0, 0), at (x_{i},
y_{i})) with
Your rope currently has length R, but you may choose to cut it down to
any shorter length r (including nonintegers) before you start swinging.
As such, you will start at
What is the maximum number of bends you can put into the rope with one swing? A bend happens when your rope touches a target and then rotates some nonzero number of degrees around that target. The rope will always remain perfectly straight (again, this is possible because you are a ninja), except at bends.
Example
In the example above, there are 6 points:
If, however, you cut the rope by 0.18 units, you will not have enough
length to reach point
(0, 0)(12, 4)(14, 5)(13, 7)(12, 4)(14, 5)and will end up orbiting point
Case #1 in the sample input below represents this example.
Input
The input will start with a line containing T, the number of test cases to follow. Each test case will start with two integers together on a line: N and R. The next N lines will each contain a pair of integers  x_{i} and y_{i}  the coordinates of the targets, starting with the target at (0, 0).
Output
For each test case, output a line of the form "Case #C: k", where C is the 1based case number, and k is the maximum number of bends that can be made in the rope in one swing.Limits
1 ≤ T ≤ 100Small dataset
1 ≤ N ≤ 10Large dataset
1 ≤ N ≤ 1,000Sample
Input 
Output 
6

Case #1: 5

Points  Correct  Attempted 

11pt  6  8 
23pt  0  2 