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: Wrong Answer)

N, M = gets.split(' ').map(&:to_i)

fib = 1.upto(N).reduce([1, 1]){ |last, cur| last << last[-1] + last[-2]}
p fib

a = []
M.times do |i|
  a << gets.to_i
end

last = 0
arr = []
a.each_with_index do |cur, i|
  break arr = [] if last == cur - 1 && !last.zero?
  arr << ((cur - last - 1 == 0) ? 1 : cur - last - 1)
  arr << N - cur if M == i + 1
  last = cur
end

if arr.size.zero?
  puts 0
else
  ans = 1
  p arr
  arr.each do |i|
    p fib[i - 1]
    ans *= fib[i - 1]
  end
  p ans % 1000000007
end