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);
$l = []; $a_b = -1; $s = 1;
$fact_l = []; $pattern_l = [];
for ($i=0; $i < $m + 1; $i++) {
  if ($i === $m) {
    $a = $n + 1;
  } else {
    fscanf(STDIN, "%d", $a);
  }
  $l[] = $a;
  $sp = $a - $a_b - 1;
  if ($sp === 0) {
    $s = 0;
    break;
  }
  $s *= $sp >= 3 ? get_pattern($sp) : 1;
  $a_b = $a;
}
echo $s % 1000000007;

function get_pattern($n) {
  global $pattern_l;
  if (!isset($pattern_l[$n])) {
    $st2_m = floor($n / 3);
    $st1_m = $n % 3;
    $pattern_l[$n] = 0;
    for ($st2=0; $st2 < $st2_m + 1; $st2++) {
      $st1 = $n - $st2 * 3;
      if ($st2 === 0 or $st1 === 0) {
        $pattern_l[$n] += 1;
      } else {
        $pattern_l[$n] += get_m_fact($st1 + $st2, $st1, $st2);
      }
    }
  }
  return $pattern_l[$n];
}

function get_m_fact($x, $y, $z) {
  return get_fact($x) / get_fact($y) / get_fact($z);
}

function get_fact($d) {
  global $fact_l;
  if (!isset($fact_l[$d])) {
    $fact_l[$d] = $d > 0 ? $d * get_fact($d - 1) : 1;
  }
  return $fact_l[$d];
}
?>