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)

chomp (my ($n, $m) = split / /, <STDIN>);
my @a;
for my $i (1..$m) {
  chomp (my $in = <STDIN>);
  push @a, $in;
}
my @b;
my ($c, $j) = (0, 0);
for my $i (0..$n) {
  if ($i == $a[$j]) {
    if ($c == 0) {
      print "0\n";
      exit;
    }
    $j++;
    push @b, $c;
    $c = 0;
  } else {
    $c++;
    push @b, $c if $i == $n;
  }
}
my @memo;
$memo[1] = 1;
$memo[2] = 1;
for my $i (3..$n) {
  $memo[$i] = $memo[$i - 1] + $memo[$i - 2];
}
my $ans = 1;
for my $i (@b) {
  $ans *= $memo[$i];
  $ans %= 1e9 + 7;
}
print "$ans\n";