Keep on Truckin'

A truck driver plans to drive along the Trans-Canada Highway from Vancouver to St. John's, a distance of $7000$ km, stopping each night at a motel.

The following motels are always available, listed by their distance in km from the starting point in Vancouver:

0, 990, 1010, 1970, 2030, 2940, 3060, 3930, 4060, 4970, 5030, 5990, 6010, 7000

More motels may be added just before the trip begins.

The driver can complete the journey only if all of the following hold:

1. each day the driver travels at least $A$ km (a company rule),
2. each day the driver travels at most $B$ km (a legal limit), and
3. every night is spent at an eligible motel (either from the fixed list above or from the additional locations given in the input).

The trip starts at km $0$ (Vancouver) and ends at km $7000$ (St. John's). Count the number of different ways the driver can choose the sequence of overnight motels so that every daily distance is between $A$ and $B$, inclusive.

For instance, with no added motels: if $A = 1$ and $B = 500$ the trip is impossible, so the answer is $0$; if $A = 970$ and $B = 1030$ there is exactly one plan; and if $A = 970$ and $B = 1040$ there are four plans. If $A = 970$, $B = 1030$ and one extra motel is added at km $4960$, there are two plans.

• The first line contains the minimum daily distance $A$.
• The second line contains the maximum daily distance $B$, with $1 \le A \le B \le 7000$; both are integers.
• The third line contains an integer $N$ ($0 \le N \le 20$), the number of additional motels.
• Each of the next $N$ lines contains one integer $m$ ($0 < m < 7000$), the distance of an additional motel from Vancouver.

No two motels are located at the same distance from Vancouver.

Print a single integer: the number of different ways the driver can choose the overnight motels to complete the trip under the given constraints.