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)

n, m = gets.split(" ").map(&:to_i)
brokens = []
brokens.push(0)
m.times do
  brokens.push(gets.to_i)
end
brokens.push(n)

brokens.reverse!

gaps = []

(brokens.length - 1).times do |index|
  if index == 0 || index == m
    gaps.push(brokens[index] - brokens[index + 1])
  else
    gaps.push(brokens[index] - brokens[index + 1] - 1)
  end
end

# puts gaps
# puts ""

sums = []
sums.push(0)
sums.push(1)
100.times do |index|
  sums.push(sums[index] + sums[index + 1])
end
# puts sums

multipliers = []

answer = 1


gaps.each do |gap|
  multipliers.push(sums[gap])
end

# puts multipliers
# puts ""

gaps.pop
gaps.shift

gaps.each do |gap|
  if gap == 0
    answer = 0
  end
end

multipliers.each do |multiplier|
  answer *= multiplier
end

puts answer  % 1000000007