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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

long pp[100001];

long p(int w) {
  
   if (pp[w]>0) return pp[w];
   pp[w]=(p(w-1)+p(w-2))%1000000007;
   return pp[w];
}

int main(){
   int n,m,a[100000],i,j,w;
   long ans;
    
   scanf("%d %d",&n,&m);
   for (i=0;i<m;i++) scanf("%d",&a[i]);
   pp[1]=pp[2]=1;
   for (i=3;i<=n;i++) pp[i]=0;
   ans=1;j=0;
   for (i=0;i<m;i++) {
      w=a[i]-j;
      if (w==0) {
         ans=0;
         break;
      }
      ans=(ans*p(w))%1000000007;
      j=a[i]+1;
   }
   w=n-j+1;
   if (w>0) ans=(ans*p(w))%1000000007;
   else     ans=0;
   printf("%d\n",ans);
   return 0;
}