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)

# 4, 0, 608200469

waru = 1_000_000_007 # あまりを出す
n, m = gets.split.map &:to_i # N段目まで行きたい
a = []
while aa = gets # 壊れてる階段
  a << aa.to_i
end
# p [n, m]
# p a

arr = Array.new(n, 0)
# arr[0] = 1
# arr[1] = 1
0.upto(n) do |i|
  if a.any?{|aa|aa == i}
    arr[i] = 0
    next
  end
  if i == 0 || i == 1
    arr[i] = 1
    next
  end
  arr[i] = arr[i-1] + arr[i-2]
end

# p arr
p (arr[-1] % waru)