**Problem H**

**Rat Attack **

**Input: **standard input

**Output: **standard
output

**Time Limit:** 7 seconds

**Memory Limit: **32 MB

Baaaam! Another deadly gas bomb explodes in Manhattan’s
underworld. Rats have taken over the sewerage and the city council is doing everything
to get the rat population under control.

As you know, Manhattan
is organized in a regular fashion with streets and avenues arranged like a
rectangular grid. Waste water drains run beneath the streets in the same
arrangement and the rats have always set up their nests below street
intersections. The only viable method to extinguish them is to use gas bombs
like the one which has just exploded. However, gas bombs are not only dangerous
for rats. The skyscrapers above the explosion point have to be evacuated in
advance and so the point of rat attack must be chosen very carefully.

The gas bombs used are built by a company called American
Catastrophe Management (ACM) and they are sold under the heading of
“smart rat gas”. They are smart because — when fired —
the gas spreads in a rectangular fashion through the under street canals. The
strength of a gas bomb is given by a number d which specifies the rectangular
“radius” of the gas diffusion area. For example, Figure 2 shows
what happens when a bomb with d = 1 explodes.

**The Problem**

The area of interest consists of a discrete grid of 1025
× 1025 fields. Rat exterminator scouts have given a detailed report on
where rat populations of different sizes have built their nests. You are given
a gas bomb with strength d and your task is to find an explosion location for
this gas bomb which extinguishes the largest number of rats.

The best position is determined by the following criteria:

• The sum of all rat population sizes within the
diffusion area of the gas bomb (given by d) is maximal.

• If there is more than one of these best positions
then the location with the “minimal” position will be chosen.
Positions are ordered first by their x coordinate and second by their y
coordinate.

Formally, given a location (x1, y1) on the grid, a point
(x2, y2) is within the diffusion area of a gas bomb with strength d if the
following equation holds:

**max (abs(x2 -
x1), abs (y2 - y1)) <= d**

### Input

The first line contains the number of scenarios in the
input.

For each scenario the first line contains the strength d of the gas bomb
in the scenario (1
<= d <= 50). The second
line contains the number n (1
<= n <= 20000) of rat
populations. Then for every rat population follows a line containing three
integers separated by spaces for the position (x, y) and “size” i of the
population (1 <= i <= 255). It is
guaranteed that position coordinates are valid (i.e., in the range between 0
and 1024) and no position is given more than once.

### Output

For every problem print a line containing the x and y
coordinate of the chosen location for the gas bomb, followed by the sum of the
rat population sizes which will be extinguished. The three numbers must be
separated by a space.

### Sample Input

1

1

2

4 4
10

6 6
20

### Sample Output

5 5
30

**TUD Programming
Contest**