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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(let* ((n (read))
       (m (read))
       (lst (loop :repeat m :collect (read)))
       (arr (make-array (+ 2 n) :element-type 'fixnum :initial-element 0)))
  (setf (aref arr 0) 1)
  (loop :for k :from 0 :upto (1- n)
        :do (if (or (not lst) (not (= k (car lst))))
                (progn (setf (aref arr (+ 1 k))
                             (mod (+ (aref arr (+ 1 k)) (aref arr k)) 1000000007))
                       (setf (aref arr (+ 2 k))
                             (mod (+ (aref arr (+ 2 k)) (aref arr k)) 1000000007)))
                (progn (setf lst (cdr lst))
                       (setf (aref arr k) 0))))
  (princ (aref arr n)))