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: Runtime Error)

def combi(n,k)
  r = 1
  (1..k).each{|i| r *= n; n -= 1; r /= i }
  r
end

def count_interval(x,y)
  max_k = (y-x)/2
  count = 0
  (0..max_k).each { |k|
    count += combi(y-x-k,k)
    }
  count
end

n,m=gets.chomp.split().map(&:to_i)
a=[]
m.times{a.push(gets.chomp.to_i)}
total = count_interval(0,a[0]-1)
(0..(m-2)).each do |l|
  if a[l+1] - a[l] <=1 then
    total = 0
    break
  end
  total *= count_interval(a[l]+1,a[l+1]-1) % 1_000_000_007
  total %= 1_000_000_007 
end
  
unless total == 0
  total *= count_interval(a[m-1]+1,n) % 1_000_000_007
  total %= 1_000_000_007 
end
puts total