Multikill

A zombie outbreak has begun. Zombies go down easily, but ammunition is scarce, so no round can be wasted. The strongest defensive weapon on hand is an automated grenade launcher that spots zombies at long range. What is missing is the code that picks a blast point so a single round takes out as many zombies as possible.

Each group of zombies comes with a kill radius and the position of every zombie in the group. Pick one blast point and report the largest number of zombies a single round can kill. A zombie dies when its distance from the blast point is at most the kill radius. The blast point may be any coordinate on the plane, and it is not restricted to a zombie position.

The first line contains the number of groups $C$ ($1 \le C \le 20$).

Each group begins with a line holding the kill radius $R$ and the zombie count $N$. $R$ is a real number with $0 < R \le 1000.0$, and $N$ is an integer with $0 \le N \le 25$. The next $N$ lines each hold one zombie position as coordinates $X$ and $Y$ ($-10^6 \le X, Y \le 10^6$). The radius and the coordinates are given in meters, and both may carry a decimal point.

C
R N
X1 Y1
...
XN YN

For each group, print the largest number of zombies that a single round can kill, one line per group.