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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int n,m;
  cin>>n>>m;
  vector<int> a(m);
  for (size_t i = 0; i < m; i++) {
    cin>>a[i];
  }
  vector<int> a2(m);
  for (size_t i = 0; i < m; i++) {
    if(i==0){
      a2[i]=a[i];
    }else{
      a2[i]=a[i]-a[i-1]-1;
    }
  //  cout<<a2[i]<<endl;
  }

  if(m==0){
    a2.push_back(n+1);
  }else{
    a2.push_back(n-a[m-1]);
  //  cout<<n-a[m-1]<<endl;
  }

  vector<long> step12(n+1);
  step12[0]=1;step12[1]=1;step12[2]=2;
  for (size_t i = 3; i < n+1; i++) {
    step12[i]=(step12[i-1]+step12[i-2])%1000000007;
  }
  long ans = 1;
  for (size_t i = 0; i < m+1; i++) {
    if(a2[i]==0){
      cout<<0;return 0;
    }
    ans*=step12[a2[i]-1];
    ans%=1000000007;
  }
  cout<<ans;
}