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: Accepted)

N,M,*as=$<.read.split.map(&:to_i)
mod=10**9+7
fib = [1,1]
2.upto(N) do |i|
    fib << fib[i-2]+fib[i-1]
end
prev = 0
ret = 1
as << N+1
as.each do |a|
    if prev == a
        puts 0
        exit
    end
    ret = ret * fib[a-prev-1]
    prev = a+1
end
puts ret%mod



# 1

# 1 1
# 2

# 1 1 1
# 1 2
# 2 1

# 1 1 1 1
# 1 1 2
# 1 2 1
# 2 1 1
# 2 2

# 1 1 1 1 1
# 1 1 1 2
# 1 1 2 1
# 1 2 1 1
# 2 1 1 1
# 2 2 1
# 2 1 2
# 1 2 2

# 1 1 1 1 1 1
# 1 1 1 1 2
# 1 1 1 2 1
# 1 1 2 1 1
# 1 2 1 1 1
# 2 1 1 1 1
# 1 1 2 2
# 1 2 1 2
# 1 2 2 1
# 2 1 1 2
# 2 1 2 1
# 2 2 1 1
# 2 2 2