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<string>
#include<vector>
#include<algorithm>
#include<unordered_map>
#include<stdio.h>
using namespace std;
typedef  unsigned long long ll;
ll mod = 1000000007;
ll N;
ll M;
ll ans = 0;



int main(){
	
	cin>>N;
	
	cin>>M;
	ll des[M];
	ll dp[N+2];
	
	for(ll i = 0; i < N; i++){
		if(i < M){
			cin>>des[i];
			if(des[i] - 1 == des[i - 1] and i and i < N-1){
				cout<<0<<endl;
				return 0;
			}
		}
		dp[i] = 0;
	}
	ll s= 0;
	dp[0] = 1;
	
	for(ll i = 0; i < N; i++){
		//if(i > des[s])s++;
		if(i == des[s]){
			dp[i] = 0;
			if(s < M - 1)s++;
			continue;
		}
		
		dp[i] %= mod;
		dp[i+1]=(dp[i+1]%mod+dp[i]%mod)%mod;
		dp[i+2]=(dp[i+2]%mod+dp[i]%mod)%mod;

	}
	cout<<(dp[N - 1]%mod + dp[N - 2] % mod)%mod<<endl;
}