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>
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#include <ext/pb_ds/assoc_container.hpp>

#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

using namespace __gnu_pbds;
#define lli long long int
#define ulli unsigned long long int
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define pf pop_front()
#define lb lower_bound
#define ub upper_bound
#define bs binary_search
#define max3(a,b,c) max(a,max(b,c))
#define loopl(i,a,b) for(lli i=a;i<b;i++) 
#define loop(i,a,b) for(int i=a;i<b;i++)
#define mod 1000000007
#define mo 998244353
#define inf 1000000000000000
#define lld long double
#define pll pair<long long int,long long int>
#define vll vector<lli>
#define eps 0.000001
#define ms 16
#define endl '\n'

 
using namespace std ;
 
#define N 100005

typedef tree<lli,null_type,less<lli>,rb_tree_tag,
tree_order_statistics_node_update> indexed_set;

int main()
{  
/////////////////////////////////////
    
    fastio;

    lli n,m;
    cin>>n>>m;

    lli dp[n+1]={0};

    lli a[m];
    loopl(i,0,m) cin>>a[i];

    lli ptr=0;

    dp[0] = 1;
    if(a[0] == 1)
    {
        dp[1] = 0;
        ptr++;
    }

    else
    {
        dp[1]=1;
    }

    loopl(i,2,n+1)
    {
        if(ptr<m && a[ptr] ==i) {ptr++;continue;}

        else
            dp[i] = (dp[i-1]+dp[i-2])%mod;
    }

    cout<<dp[n];


}