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: Time Limit Exceeded)

N,M = gets.chomp.split(" ").map(&:to_i)
arr = readlines.map{|n| n.chomp.to_i}
# p arr

class Integer
    def combination(k)
      return 1 if k.zero?
  
      (self - k + 1..self).inject(:*) / k.factorial
    end
  
    def permutation(k)
      return 1 if k.zero?
  
      (self - k + 1..self).inject(:*)
    end
  
    def factorial
      return 1 if self.zero?
  
      (1..self).inject(:*)
    end
end


def step_sum(step)
    sum = 0
    return 1 if step == 0
    step.times do |i|
        one = i
        two = step - i
        break if step/2 > two
        sum += two.combination one
    end
    return sum
end

prev = 0
ans = 1
arr << N+1
arr.each do |cur|
    if prev == cur
        ans = 0
        break
    end
    step = cur-1-prev
    
    ans*=step_sum(step)
    # p [step, ans]
    prev = cur+1
end

puts ans % 1000000007