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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std; 
#define int int64_t
#define itn int
#define fi first
#define se second 
signed main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n,m,a;
  int dp[1000000]={};
  cin>>n>>m;
  dp[0]=1;
  dp[1]=1;
  for(int i=0;i<m;i++){
    cin>>a;
    dp[a]=-1;
  }
  for(int i=2;i<=n;i++){
    if(dp[i]!=-1){
      if(dp[i-1]!=-1) dp[i]+=dp[i-1];
      if(dp[i-2]!=-1) dp[i]+=dp[i-2];
      dp[i]%=1000000007;
    }
  }
  cout<<dp[n]<<"\n";
}