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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%d %d", $n, $m);
$a_b = -1; $s = 0;
for ($i=0; $i < $m + 1; $i++) {
  if ($i === $m) {
    $a = $n + 1;
  } else {
    fscanf(STDIN, "%d", $a);
  }
  $sp = $a - $a_b - 1;
  if ($sp === 0) {
    $s = 0;
    break;
  }
  $s += $sp >= 3 ? floor(($sp - 1) / 2) : 0;
  $a_b = $a;
}
echo $s == 0 ? 0 : pow(2, $s) % 1000000007;
?>