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 = 1000000007
N, M = gets.split.map(&:to_i)
a = []
c = []
c[0] = 1
M.times do |i|
  a[i] = gets.to_i
end

i=0
1.upto N do |j|
  # jが通れない床の場合c[j]=0
  if a[i] == j
    c[j] = 0
    i += 1
  # jが通れる床の場合c[j]=c[j-1]+c[j-2]
  else
    # 床1が通れるならc[1]=1
    if j == 1
      c[j] = 1
    else
      c[j] = (c[j-1] + c[j-2]) % MOD
    end
  end
  # 2回連続0なら今後もずっと0なので
  if c[j] == 0 and c[j-1] == 0
    # puts "#{c}"
    puts 0
    exit
  end
end

# puts "#{c}"
puts c[N]