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 <iostream>
#include<algorithm>
#include<cstdio>
#include<math.h>
#define mod 1000000007
using namespace std;
int main()
{
    //f[n]=f[n-1]+f[n-2];
    long long a[100000+5];
    int n,i,m,x1,x2,flag=1,s[100000+5];
    a[1]=1,a[2]=1;
    a[0]=1;
    for(i=3;i<100005;i++)
    {
        a[i]=a[i-1]+a[i-2];
        a[i]%=mod;
    }
    scanf("%d %d",&n,&m);
    for(i=0;i<m;i++)
    {
        scanf("%d",&s[i]);
        if(i!=0&&s[i]-s[i-1]==1)
        {
            flag=0;
            break;
        }
    }
    if(flag==0)
        printf("0\n");
    else
    {
        long long int ans=0;
        for(i=0;i<m;i++)
        {
            if(i==0)
                ans+=a[s[0]-0];
            else
            {
                ans*=a[s[i]-1-s[i-1]];
                ans%=mod;
            }
        }
        ans*=a[n-s[i-1]];
        ans%=mod;
        printf("%lld\n",ans);

    }
    return 0;
}