There is a long electrical wire of length $\ell $ centimetres between two poles
where birds like to sit. After a long day at work you like to
watch the birds on the wire from your balcony. Some time ago
you noticed that they don’t like to sit closer than
$d$ centimetres from each
other. In addition, they cannot sit closer than 6 centimetres
to any of the poles, since there are spikes attached to the
pole to keep it clean from faeces that would otherwise damage
and weaken it. You start wondering how many more birds can
possibly sit on the wire.
Task
Given numbers $\ell $
and $d$, how many
additional birds can sit on the wire given the positions of the
birds already on the wire? For the purposes of this problem we
assume that the birds have zero width.
Input
The first line contains three space separated integers: the
length of the wire $\ell
$, distance $d$ and
number of birds $n$
already sitting on the wire. The next $n$ lines contain the positions of the
birds in any order. All number are integers, $1\leq \ell , d\leq 1\, 000\, 000\,
000$ and $0\leq n\leq 20\,
000$. (If you have objections to the physical
plausibility of fitting that many birds on a line hanging
between two poles, you may either imagine that the height of
the line is 0 cm above ground level, or that the birds are ants
instead.) You can assume that the birds already sitting on the
wire are at least 6 cm from the poles and at least $d$ centimetres apart from each
other.
Output
Output one line with one integer – the maximal number of
additional birds that can possibly sit on the wire.
Sample Input 1 
Sample Output 1 
22 2 2
11
9

3

Sample Input 2 
Sample Output 2 
47 5 0

8
