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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use strict;
use warnings;

my ($n, $m) = split /\s/, <>;

my @a = ();
foreach (1 .. $m) {
	chomp(my $a = <>);
	push @a, $a;
}
push @a, 999999;

if ($n == 1) {
	print 1, "\n";
	exit;
} elsif ($n == 2) {
	if (@a == 0) {
		print 2, "\n";
	} else {
		print 1, "\n";
	}
	exit;
}

my $a = shift @a;
my $p1 = 1;
my $p2 = 1;
if ($a == 1) {
	$p2 = 0;
	$a = shift @a;
}

foreach my $i (2 .. $n) {
	if ($a == $i) {
		$p1 = $p2;
		$p2 = 0;
		$a = shift @a;
	} else {
		($p1, $p2) = ($p2, $p1 + $p2);
	}
	
	if ($p1 == 0 and $p2 == 0) {
		last;
	}
	$p2 = $p2 % 1000000007;
}

print $p2, "\n";