The government in a foreign country is looking into the
possibility of establishing a subway system in its capital.
Because of practical reasons, they would like each subway line
to start at the central station and then go in a straight line
in some angle as far as necessary. You have been hired to
investigate whether such an approach is feasible. Given the
coordinates of important places in the city as well as the
maximum distance these places can be from a subway station
(possibly the central station, which is already built), your
job is to calculate the minimum number of subway lines needed.
You may assume that any number of subway stations can be built
along a subway line.
Input
The first line in the input file contains an integer
$N$, the number of data
sets to follow. Each set starts with two integers, $n$ and $d$ ($1
\le n \le 500$, $0 \le d
< 150$). $n$ is
the number of important places in the city that must have a
subway station nearby, and $d$ is the maximum distance allowed
between an important place and a subway station. Then comes
$n$ lines, each line
containing two integers $x$ and $y$ ($100 \le x, y \le 100$), the
coordinates of an important place in the capital. The central
station will always have coordinates $0,0$. All pairs of coordinates within
a data set will be distinct (and none will be $0,0$).
Output
For each data set, output a single integer on a line by
itself: the minimum number of subway lines needed to make sure
all important places in the city are at a distance of at most
$d$ from a subway
station.
Sample Input 1 
Sample Output 1 
2
7 1
1 4
3 1
3 1
2 3
2 4
2 2
6 2
4 0
0 4
12 18
0 27
34 51

4
2
