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)

N,M = gets.chomp.split(" ").map(&:to_i)
broken_stairs = []
ans = 0
flg = true
for i in 0..M-1 do
    bs = gets.chomp.to_i 
    broken_stairs[i] = bs - 1
    if i >= 1
        if broken_stairs[i] < broken_stairs[i-1]
            if broken_stairs[i-1] - broken_stairs[i] == 1
                flg = false
            end
        else
            if broken_stairs[i] - broken_stairs[i-1] == 1
                flg = false
            end
        end
    end 
end

for i in 1..N-1 do
    if flg == false
        break
    end
    if broken_stairs.include?(i)
        # Nothing
    elsif i % 2 == 1
        ans = ans * 2
    end
end
if flg == true
    puts ans 
else
    puts 0
end