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.split.map(&:to_i)
aa =
  readlines.map do |i|
    i.chomp.to_i
  end.to_a

DIV = 1_000_000_007
cnt = 1
step = Hash.new(0)
st = 0
aa.each do |a|
  if (a-1)-st < 0
    # できない
    puts 0
    exit
  end
  step[(a-1)-st]+=1
  st = a+1
end
# 最後の水から最後の階段まで
step[n-st]+=1 if st<n #TODO あってる？

step.each_pair do |key, val|
  #stepの組み合わせ数
  cnt_combi = 0

  jump = key / 2
  tmp = 0
  0.upto(jump) do |i|
    # jumpとstepの合計の中からjumpを取る組み合わせ
    # 計算量気にして前回ループの結果を使う
    if i==0
      tmp = 1
    elsif i==1
      tmp = key-1
    else
      a=key-2*i+i
      tmp = tmp*(a-i+1)*(a-i+2)/(a+1)/i
    end
    cnt_combi += tmp
  end

  temp = 1
    1.upto(val) do
      temp = temp * cnt_combi % DIV
    end
  cnt = cnt * temp % DIV
end

puts cnt % DIV