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)

class MyLib
  def combi(x,y)
    y=x-y if 2*y > x
    return 1 if y == 0
    ((x-y+1)..x).reduce(&:*)/((1..y).reduce(&:*))
  end
end

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

cnt = 1
st = 0
aa.each do |a|
  en = a - 1
  if st > en
    # できない
    cnt = 0
    break
  end
  #st-enの組み合わせ数
  cnt_combi = 0

  step = en - st
  jump = step / 2
  0.upto(jump) do |i|
    # jumpとstepの合計の中からjumpを取る組み合わせ
    cnt_combi += MyLib.new.combi(step-2*i+i, i)
    #puts cnt_combi
  end
  cnt = cnt * cnt_combi % 1_000_000_007

  st = a + 1
end

# aa最後よりあと
if st>n
  puts cnt % 1_000_000_007
  exit
end

en = n
#st-enの組み合わせ数
cnt_combi = 0
step = en - st
jump = step / 2
0.upto(jump) do |i|
  # jumpとstepの合計の中からjumpを取る組み合わせ
  cnt_combi += MyLib.new.combi(step-2*i+i, i)
end
cnt = cnt * cnt_combi % 1_000_000_007

puts cnt % 1_000_000_007