## Problem Description

You want to destroy a bridge with bombs. The lower-left corner of the bridge is at (0,
0) and the upper-right corner is at (w, l). There are already b bombs exploded, the
i-th bomb created a hole of radius ri centering at (xi, yi). You want to throw exactly
one more bomb so that the bridge is split into two connected parts(though the two
parts can share a finite number of points), so that no one can go through the bridge
from y = 0 to y = l.
Your task is to find the minimal radius of the last bomb to split the bridge, assuming
that the last bomb can explode precisely at the position you want (possibly at noninteger
coordinates).
Note that you are only allowed to use bombs with integer radius. That is, even if a
bomb with radius 1.01 is sufficient, you have to use a bomb with radius 2, since you
only have bombs with integer radius.
## Input

The first line contains t (1 ≤ t ≤ 10), the number of test cases followed. Each test case
begins with three integers w, l, b(1 ≤ w, l ≤ 100, 0 ≤ b ≤ 10). Each of the following b
lines contains three integers integers xi, yi, ri(0 ≤ x ≤ w, 0 ≤ y ≤ l, 0 < r ≤ 100). The
bridge is guaranteed to be connected before the last bomb.

## Output

For each test case, print the minimal radius of the last bomb.

## Sample Input

3
100 100 2
15 50 20
90 50 30
100 100 1
50 50 40
100 100 1
10 50 10

## Sample Output

13
50
40

## Source

2009 NIT Cup National Invitation Contest Practice Session