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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

//標準入力
class Scanner {
  private $arr = [];
  private $count = 0;
  private $pointer = 0;
  public function next() {
      if($this->pointer >= $this->count) {
          $str = trim(fgets(STDIN));
          $this->arr = explode(' ', $str);
          $this->count = count($this->arr);
          $this->pointer = 0;
      }
      $result = $this->arr[$this->pointer];
      $this->pointer++;
      return $result;
  }
  public function hasNext() {
      return $this->pointer < $this->count;
  }
  public function nextInt() {
      return (int)$this->next();
  }
  public function nextDouble() {
      return (double)$this->next();
  }
}

//標準出力
class out {
    public static function println($str = "") {
        echo $str . PHP_EOL;
    }
}



$sc = new Scanner();
$N = $sc->nextInt();
$M = $sc->nextInt();
$a = array();
$flag = true;
$col = 0;
$tmp = 0;
$sum = 0;
$ans = 1;

for($i = 1;$i <= $M; $i++){
    $a[] = $sc->nextInt();
}

for($i = 1;$i < $M; $i++){
    if($M === 1){
        break;
    }
    
    if($a[$i] - $a[$i-1] === 1){
        $flag = false;
        break;
    }
}

var_dump($a);

if($flag){
    for($i = 0; $i < count($a); $i++){
        $sum = fibona($a[$i] - $tmp);
        $ans = ($ans * $sum) % 1000000007;
        $tmp = $a[$i];
        echo "sum:".$sum.PHP_EOL;
        echo "ans:".$ans.PHP_EOL;
        echo "tmp:".$tmp.PHP_EOL;
    }
    $sum = fibona($N - $tmp);
    $ans = ($ans * $sum) % 1000000007;
}else{
    $ans = 0;
}


echo $ans.PHP_EOL;



function fibona($n){
    if($n === 0){
        return 0;
    }

    if($n === 1){
        return 1;
    }
    return fibona($n -1) + fibona($n -2);
}