Alien Invasion
By Dilson Guimarães, UFMG 
Brazil
By Dilson Guimarães, UFMG Brazil
The Aliens are going to invade the earth and destroy the human race, unless you stop them. Recently, the S.B.C (Combat Brazilian System) was armed with a powerful laser gun, that will be used to kill the alien enemies. This gun destruct everything that are in a circle area of its shot. Fortunately, its possible control the shots of the gun in a way that it can choose the center and radius of the circle area that will be destructed.
Yeah, its possible to make a shot with circle area enough to destruct all alien enemies. Unfortunately, if we did that it's possible that all humanity could be destroyed. That's why you have been hired. Your job is to determine how many enemies could be killed for one shot of the laser gun without killing any human.
Observations
All man in the border of the destructed area of laser gun are also killed.
The input has many test cases. Each test case has one line with two integers, N and M (1 ≤ N, M ≤ 100), describing the number of aliens and humans, respectively. Each of its next N following lines have two integers, Xi and Yi (-106 ≤ Xi, Yi ≤ 106), representing the coordinates of the aliens. In the same way, each of next M following lines have two integers, Xi and Yi (-106 ≤ Xi, Yi ≤ 106), representing the coordinates of the humans. Besides treating about aliens, its not possible that two individuals are in the same spot. The input ends with N=M=0.
For each test case, output one integer representing the number of aliens that could be killed with one shot of the laser gun, without any human been killed.
| Input Sample | Output Sample |
|
5 1 |
5 |