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: Wrong Answer)

nm = gets.chomp.split
n = nm[0].to_i
m = nm[1].to_i

a = []
never = false
m.times do |i|
    input = gets.to_i
    if a.include?(input-1)
        never = true
        break
    end
    a << input
end

def combi count
    return count if count == 1 || 2 || 3
    return (((count - 3) ** 2) + 4)
end

if never
    puts 0
else
    sums = []
    start = 0
    a.each do |i|
        sum = combi((i-1) - start)
        sums << sum if sum != 0
        start = i+1
    end

    sums << combi(n - start)
    pro = 1
    sums.each do |i|
        pro *= i
    end
    puts pro % 1000000007
end