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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long int
#define endl "\n"
const int MOD=1e9+7;
#ifndef HOME
#define cerr if(0)cerr
#endif

int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n,m;
    cin>>n>>m;
    int a[m];
    set<int>s;
    for(int i=0;i<m;i++){
        cin>>a[i];
        s.insert(a[i]);
    }
    int dp[n+5];
    dp[0]=0;
    dp[1]=1;
    dp[2]=2;
    if(s.find(1)!=s.end()){
        //cerr<<1<<endl;
        dp[1]=0;
        dp[2]=1;
    }
    if(s.find(2)!=s.end()){
        dp[2]=0;
    }
    for(int i=3;i<=n;i++){
        if(s.find(i)!=s.end()){
            dp[i]=0;
        }else{
            dp[i]=(dp[i-1]+dp[i-2])%MOD;
        }
    }
    cout<<dp[3]%MOD<<endl;
    return 0;
    
}