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City Tour

Problem Description

There are A cities numbered from 1 to A. You have already visited M cities, the indices of which are given in an array B of M integers.

If a city with index i is visited, you can visit either the city with index i-1 (i >= 2) or the city with index i+1 (i < A) if they are not already visited. Eg: if N = 5 and array M consists of [3, 4], then in the first level of moves, you can either visit 2 or 5.

You keep visiting cities in this fashion until all the cities are not visited. Find the number of ways in which you can visit all the cities modulo 10^9+7

Problem Constraints
1 <= A <= 1000
1 <= M <= A
1 <= B[i] <= A

Input Format
The 1st argument given is an integer A, i.e total number of cities.
The 2nd argument given is an integer array B, where B[i] denotes ith city you already visited.

Output Format
Return an Integer X % (1e9 + 7), the number of ways in which you can visit all the cities.

Example Input
A = 5
B = [2, 5]

Example Output
6

Example Explanation
All possible ways to visit remaining cities are :
1. 1 -> 3 -> 4
2. 1 -> 4 -> 3
3. 3 -> 1 -> 4
4. 3 -> 4 -> 1
5. 4 -> 1 -> 3
6. 4 -> 3 -> 1

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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