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)

my($n,$m)=split/ /,<>;
my@a=<>;
@a=(-1,@a,$n+1);
my@f=(1,1);
my$ans=1;
for(my$i=1;$i<=$m+1;$i++){
 if($a[$i]==$a[$i-1]+1){
  $ans=0;
  last;
 }else{
  my$l=$a[$i]-$a[$i-1]-1;
  for(my$j=@f;$j<$l+1;$j++){
  push@f,$f[$j-2]+$f[$j-1];
  }
  $ans*=$f[$l-1];
  $ans%=1000000007
 }
}
print$ans;