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: Runtime Error)

(defun memo (fn)
    (declare (type function fn))
    (let ((table (make-hash-table :test 'equal)))
        #'(lambda (&rest rest)
              (multiple-value-bind (val found-p) (gethash rest table)
                  (if found-p
                      val
                      (setf (gethash rest table) (apply fn rest)))))))

(defun memoize (fn-name)
    (declare (type symbol fn-name))
    (setf (symbol-function fn-name) (memo (symbol-function fn-name))))

(defmacro defun-memo (fn args &body body)
    `(memoize (defun ,fn ,args . ,body)))

(defvar *mod* 1000000007)
(defparameter *unuse-lst* '())

(defun-memo find-element (elem)
    (declare (type fixnum elem))
    (not (null (find elem *unuse-lst*))))

(defun-memo rec (goal now)
    (declare (type fixnum goal now))
    (cond ((eq goal now) 1)
        ((< goal now) 0)
        ((find-element now) 0)
        (t (+ (rec goal (+ 1 now))
               (rec goal (+ 2 now))))))

(defun solve (goal)
    (declare (type fixnum goal))
    (let ((result (the fixnum (rec goal 0))))
        (print (rem result *mod*))))

(let ((goal (read))
         (num (read)))
    (dotimes (i num)
        (push (read) *unuse-lst*))
    (solve goal))