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)

MOD = (1e+9 + 7).to_i

def chcek(n, m, a)
  (m - 1).times do |i|
    if a[i + 1] - a[i] == 1 then
      return false
    end
  end
  return true
end

def main(argv)
  (n, m) = gets.chomp.split(' ').map(&:to_i)
  
  a = [-1] * m
  m.times {|i| a[i] = gets.chomp.to_i}

  a.uniq!
  m = a.size

  unless chcek(n, m, a) then
    puts 0.to_s
    return
  end
  
  dp = [0] * (n + 2)
  dp[0] = 1
  dp[1] = 1
  n.times do |i|
    dp[i + 2] = dp[i + 1] + dp[i]
  end

  c = 1
  k = 0
  m.times do |i|
    c = (c * dp[(a[i] - 1) - k]) % MOD

    k = a[i] + 1
  end
  c = (c * dp[n - k]) % MOD
  
  puts c.to_s
end

if self.to_s == 'main' then
  main(ARGV)
end