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)

inputs = Array.new
while line = $stdin.gets
  inputs << line.chomp
end

N, M= inputs[0].split(" ").map(&:to_i)
$ng_list = Hash.new
inputs[1..-1].map do |s|
  ng = s.split(" ").map(&:to_i)[0]
  $ng_list[ng] = true
end

def count(n)
  cnts = []
  i = -1
  while i < n; i += 1;
    if $ng_list[i]
      cnts[i] = 0
      next
    elsif i == 0
      cnts[i] = 1
      next
    elsif i == 1
      cnts[i] = 1
      next
    else
      res = cnts[i - 1] + cnts[i - 2]
      cnts[i] = res
      next
    end
  end

  cnts.last
end

p count(N) % 1000000007