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"
using namespace std;
#define rep(i,a,n) for(ll i=a;i<n;i++)
#define ALL(s) s.begin(),s.end()
#define P pair<ll,ll>
#define vl vector<ll>
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvl vector<vector<ll>>
#define print(n) cout<<n<<endl
const int M=100010;
const int inf=1000000007;
const long long INF=1000000000000000007;
using ll=long long;
int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};


int main(){
	int n,m,a;
	bool f[M];
	rep(i,0,M)f[i]=true;
	cin>>n>>m;
	rep(i,0,m)cin>>a,f[a]=false;
	ll dp[M]={};
	dp[0]=1;
	if(f[1]==true?dp[1]=1:dp[1]=0);
	rep(i,2,n+1){
		if(f[i]==true)dp[i]=dp[i-1]+dp[i-2];
		else dp[i]=0;
		dp[i]%=1000000007;
	}
	print(dp[n]);
}