Problem:
Score : 300 points

Problem Statement

There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0-th step.
He can climb up one or two steps at a time.

However, the treads of the a_1-th, a_2-th, a_3-th, \ldots, a_M-th steps are broken, so it is dangerous to set foot on those steps.

How many are there to climb up to the top step, that is, the N-th step, without setting foot on the broken steps?
Find the count modulo 1\ 000\ 000\ 007.

Constraints

1 \leq N \leq 10^5

0 \leq M \leq N-1

1 \leq a_1 < a_2 < ... < a_M \leq N-1

Input

Input is given from Standard Input in the following format:

N M
a_1
a_2
.
.
.
a_M

Output

Print the number of ways to climb up the stairs under the condition, modulo 1\ 000\ 000\ 007.

Sample Input 1

6 1
3

Sample Output 1

4

There are four ways to climb up the stairs, as follows:

0 \to 1 \to 2 \to 4 \to 5 \to 6

0 \to 1 \to 2 \to 4 \to 6

0 \to 2 \to 4 \to 5 \to 6

0 \to 2 \to 4 \to 6

Sample Input 2

10 2
4
5

Sample Output 2

0

There may be no way to climb up the stairs without setting foot on the broken steps.

Sample Input 3

100 5
1
23
45
67
89

Sample Output 3

608200469

Be sure to print the count modulo 1\ 000\ 000\ 007.

Solution in Julia (0.5.0) (judge verdict: Accepted)

function main()
  
  (N, M) = map(x -> parse(Int, x), split(readline()))
  
  a = zeros(Int, 2N)
  for i in 1:M
    a[i] = parse(Int, readline()) + 1
  end
    
  ans = zeros(Int, 2N)
  num = 1
  
  for i in 1:N+1
    if i == 1
      ans[i] = 1
    elseif i == 2
      if a[num] == 2
        ans[i] = 0
        num += 1
      else
        ans[i] = 1
      end
    elseif a[num] == i
      num += 1
    else
      ans[i] = ans[i-1] + ans[i-2]
      ans[i] %= 1000000007
    end
  end
  
  println(ans[N+1])
  
end

main()