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<iostream>
#include<math.h>
#include<vector>
#include<algorithm>
#include<string.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
int main(){
	int n,m;
	cin>>n>>m;
	vector<long long int> map(n+1,0);
	if(m==0){

		map[0]=1,map[1]=1;
		for(int k=2;k<=n;k++){
			map[k]=(map[k-1]%1000000007)+(map[k-2]%1000000007);
		}
	cout<<map[n]%1000000007<<endl;









	}else{
	vector<int> a(m);
	rep(i,m) cin>>a[i];
	int head=0;
	map[0]=1;
	if(a[head]==1){
		map[1]=0;
		while(a[head]==1&&head<m) head++;
	}else{
		map[1]=1;
	}

	for(int k=2;k<=n;k++){
		if(a[head]==k){
			map[k]=0;
			while(a[head]==k&&head<m)head++;
		}else{
			map[k]=(map[k-1]%1000000007)+(map[k-2]%1000000007);
		}
	}
	cout<<map[n]%1000000007<<endl;
	}



	return 0;
}