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.chomp.split.map(&:to_i)
a = []
m.times { a << gets.chomp.to_i }
# p n
# p m
# p a
$nongap = []
$nongap << 0
$nongap << 1
$nongap << 2
def nongap_step(n)
  return $nongap[n] if $nongap[n]
  if n > 1 then
    r = nongap_step(n-1) + nongap_step(n-2)
    $nongap[n] = r % 1000000007
    return r
  else
    return 0
  end
end
if m == 0 then
  q = nongap_step(n)
else
  q = nongap_step(a[0])
  (1..m-1).each do |x|
    q = q * nongap_step(a[x] - a[x-1] - 1)
    q = q % 1000000007 
  end
end
puts q