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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'pp'

n, m = gets.chomp!.split(" ").map!(&:to_i)
a = Array.new(0, n + 2)

before = -1
z = false

memo_a = {}

a[0]= 0
1.upto(m) do |i|
    a[i] = gets.chomp!.to_i
    memo_a[a[i]] = a[i]
    if before + 1 == a[i]
        z = true
        break
    end
    before = a[i]
end
a[m+1]=n+1

tree = {
    1 => 1,
    2 => 2
}

if z 
    puts 0
else
    dan_max = 0
    dan = a.each_cons(2).map do |s, e|
        d = (e-s)-2
        if d > dan_max
            dan_max = d
        end 
        d
    end

    if dan_max >= 3
        3.upto(dan_max) do |x|
            tree[x] = tree[x-1] + tree[x-2]
        end
    end

    #pp tree
    #pp dan

    sum = (dan.inject(1) {|sum, x|
        if x < 0
            sum
        else
            sum *= tree[x]
        end
    }) 

    puts sum % 1_000_000_007
end