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;
const int mod=1000000007;
int a[100005],n,m;
long long t[100005];
int main()
{
//freopen("in.txt","r",stdin);
    t[0]=t[1]=1;
    for(int i=2;i<=100001;i++) t[i]=(t[i-1]+t[i-2])%mod;
    scanf(" %d %d",&n,&m);
    int x,is=1,k=1;
    long long ans=1;
    for(int i=1;i<=m;i++) scanf(" %d",&a[i]);
    sort(a+1,a+m+1);
    for(int i=2;i<=m;i++) if(a[i]==a[i-1]+1) is=0;
    if(!is) ans=0;
    else{
        a[0]=0;a[m+1]=n;
        for(int i=1;i<=m+1;i++){
            ans = (ans*t[a[i]-a[i-1]-1])%mod;
        }
    }
    cout<<ans<<endl;
    return 0;
}