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)

def count_combination(array)
  # p array
  length = array.length
  num_of_one = array.count(1)
  minor = [num_of_one, length - num_of_one].min
  if minor == 0
    1
  elsif minor == 1
    length
  else
    bunbo = bunshi = 1
    minor.times do |i|
      bunbo  *= (length - i)
      bunshi *= (minor - i)
    end
    # p bunbo/bunshi
    bunbo / bunshi
  end
end

def count_patterns(num)
  if num.even?
    pattern = [2] * (num/2)
  else
    pattern = [1] + [2] * (num/2)
  end
  count = 0
  while true
    count += count_combination(pattern)
    if pattern.include?(2)
      pattern.delete_at(pattern.index(2))
      pattern = pattern + [1, 1]
    else
      break
    end
  end
  count
end

n, m = gets.split.map(&:to_i)
brokens = readlines.map(&:to_i)
brokens << n+1
current = 0 # 今いる場所は0。
count = 1 # 0にいる方法は1通り。
brokens.each do |broken|
  target = broken - 1
  if current > target
    count = 0
    break
  elsif current < target
    count = count * count_patterns(target - current) % 1000000007
  end
  current = target + 2
end
puts count