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)

n, m = gets.split.map(&:to_i)
as   = m.times.map{ gets.to_i }
=begin
dp = Array.new(n+1){0}
dp[0]= 1

0.upto(n-1) do | i |
  if dp[i] == 0
    if dp[i-1] == 0
      p 0
      exit
    end
    next
  end
  dp[i+1] += 1 unless as.include? i+1
  break if i==n-1
  dp[i+2] += 1 unless as.include? i+2
end

# 0が出たところで配列を区切る.
dp = dp.join.split('0')
sizes = []
dp.map{|d|sizes << d.size}
p sizes
=end
before = -1
as.each do | a |
  if before == a-1
    p 0
    exit
  end
  before = a
end

sizes = []
0.upto(as.size-1) do | i |
  if sizes.empty?
    sizes << as[i]
    next
  end
  sizes << (as[i]-as[i-1]-1)
end
sizes << n - as[-1]

def fibo(n)
  return 0 if n == 0
  return 1 if n == 1
  ary = [0, 1]

  2.upto(n) do | i |
    tmp = ary[i-1] + ary[i-2]
    ary.push(tmp)
  end
  return ary
end

fibo = fibo(sizes.max)

ans = 1
sizes.each do | s |
  ans = ans * fibo[s]
end
p ans%1000000007