Problem : Colliding ants
## Problem A: Ants

An army of ants walk on a horizontal pole of length *l* cm,
each with a constant speed of 1 cm/s. When a walking ant reaches an
end of the pole, it immediatelly falls off it. When two ants meet
they turn back and start walking in opposite directions. We know the
original positions of ants on the pole, unfortunately, we do not know
the directions in which the ants are walking. Your task is to compute
the earliest and the latest possible times needed for all ants to fall
off the pole.
The first line of input contains one integer giving the number of
cases that follow. The data for each case start with two integer
numbers: the length of the pole (in cm) and *n*, the number of
ants residing on the pole. These two numbers are followed by
*n* integers giving the position of each ant on the pole as the
distance measured from the left end of the pole, in no particular
order. All input integers are not bigger than 1000000 and they are
separated by whitespace.

For each case of input, output two numbers separated by a single
space. The first number is the earliest possible time when all ants
fall off the pole (if the directions of their walks are chosen
appropriately) and the second number is the latest possible such time.

### Sample input

2
10 3
2 6 7
214 7
11 12 7 13 176 23 191

### Output for sample input

4 8
38 207

*Piotr Rudnicki*

Waterloo Local - Sep 19, 2004