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: Wrong Answer)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

(deftype int32 () '(signed-byte 32))
(deftype int64 () '(signed-byte 64))


;;macros
(defmacro println (n)
  `(format t "~a~%" ,n))
(defmacro vint-out (vec)
  `(progn
     (rep i (length ,vec)
          (princ (vref ,vec i))
          (princ " "))
     (fresh-line)))
(defmacro aif (test-form then-form &optional else-form)
  `(let ((it ,test-form))
     (if it ,then-form ,else-form)))

;;vector
(defmacro vec (type &optional (num 100) (val 0))
  (let* ((g (gensym)))
    `(let* ((,g ,num))
       (make-array ,g :element-type ',type :initial-element ,val
                   :adjustable nil :fill-pointer ,g))))

(defmacro double-vec (type &optional (dim1 100) (dim2 100) (val 0))
  `(make-array '(,dim1 ,dim2) :element-type ',type :initial-element ,val))

(defmacro vint (&optional (num 0) (val 0))
  `(vec int32 ,num ,val))

(defmacro double-vec (type &optional (dim1 100) (dim2 100) (val 0))
  `(make-array '(,dim1 ,dim2) :element-type ',type :initial-element ,val))

(defmacro vref (vector pos &optional value)
  (let ((g (gensym)))
    `(let ((,g ,value))
       (if ,g
           (setf (aref ,vector ,pos) ,g)
           (aref ,vector ,pos)))))

(defmacro chvar (sym comp predicate)
  (let ((g (gensym)))
    `(let ((,g ,comp))
       (if (or (null ,sym) (not (funcall ,predicate ,sym ,g)))
           (setf ,sym ,g)))))

(defmacro chmax (sym comp &optional (predicate #'>))
  `(chvar ,sym ,comp ,predicate))

(defmacro chmin (sym comp &optional (predicate #'<))
  `(chvar ,sym ,comp ,predicate))

(defmacro defchangef (name op default-val)
  `(defmacro ,name (var &optional (val ,default-val))
     `(setq ,var (,',op ,val ,var))))
(defmacro read-str ()
  `(write-to-string (read)))

;;本体
(defconstant *mod* 1000000007)
(defvar n (read))
(defvar m (read))
(defvar fib
  (make-array (1+ n)))

(vref fib 0 1)
(vref fib 1 1)
(loop for i from 2 to n
   do (vref fib i (mod
                   (+ (vref fib (1- i))
                      (vref fib (- i 2)))
                   *mod*)))
(vref fib 1 0)


(defun main ()
  (let ((ans 1) (pos 0) next)
    (dotimes (i m)
      (setf next (1- (read)))
      (if (< (- next pos) 0)
          (setf ans 0)
          (setf ans (mod (* ans (vref fib (- next pos))) *mod*)))
      (setf pos (+ 2 next)))
    (setf ans (mod (* ans (vref fib (- n pos))) *mod*))
    (println ans)))

#-swank(main)