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.
Input
The first line of input contains one integer giving the
number of cases that follow, at most 100. The data for each
case start with two integer numbers: the length $l$ 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 between $0$
and $1\, 000\, 000$ and
they are separated by whitespace.
Output
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 1 
Sample Output 1 
2
10 3
2 6 7
214 7
11 12 7 13
176 23 191

4 8
38 207
