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: Accepted)

MOD_SIZE = 1_000_000_007

N, M = gets.chomp.split(' ').map(&:to_i)
brokens = (M.times.map { gets.to_i }).uniq.sort
brokens.unshift(-1)
brokens.push(N+1)

$memo = {}
$memo[0] = 1
$memo[1] = 1
2.upto(N) do |i|
  $memo[i] = ($memo[i-2] + $memo[i-1]) % MOD_SIZE
end

def count_step_patterns(steps)
  return 1 if steps <= 1
  return $memo[steps] if $memo.key?(steps)
  $memo[steps] = count_step_patterns(steps-1) + count_step_patterns(steps-2)
end

cannot_reach = brokens.inject(nil) { |before, value|
  next value if before.nil?
  break nil if before + 1 == value
  value
}.nil?

if cannot_reach
  puts 0
else
  splitted = 0.upto(brokens.size-2).map { |i| brokens[i+1] - brokens[i] - 2 }
  puts splitted.inject(1) { |sum, steps| sum * $memo[steps] % MOD_SIZE }
end