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

fscanf(STDIN, "%d %d", $n, $m);
$A = [];
for ($i = 0; $i < $m; ++$i) {
    fscanf(STDIN, "%d", $a);
    $A[] = $a;
}

const MOD = 1000000007;
// フィボナッチ数列
$F = [];
function fibo($n) {
    if ($n <= 1) {
        return 1;
    }
    global $F;

    // メモ化
    if (isset($F[$n])) {
        return $F[$n];
    }
    return (fibo($n - 1) + fibo($n - 2)) % MOD;
}
for ($i = 0; $i < 100000; ++$i) {
    $F[$i] = fibo($i);
}

switch ($m) {
case 0:
    echo $F[$n] % MOD;
    break;
case 1:
    echo $F[$n - ($A[0] + 1)] * $F[($A[0] - 1) - 0] % MOD;
    break;
default:
    $flg = true;

    $sum = $F[($A[0] - 1) - 0] % MOD;
    for ($i = 0; $i < $m - 1; ++$i) {
        if ($A[$i + 1] - $A[$i] <= 1) {
            $flg = false;
            break;
        }

        $sum = $sum * $F[$A[$i + 1] - 1 - ($A[$i] + 1)] % MOD;
    }
    $sum = $sum * $F[$n - ($A[$m - 1] + 1)] % MOD;

    if ($flg) {
        echo $sum;
    } else {
        echo 0;
    }
}