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: Accepted)

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