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<iomanip>
#include<string>
#include<vector>
#include<stack>
#include<set>
#include<map>
#include<utility>
#include<algorithm>
#include<cmath>
#include<climits>
using namespace std;

#define MOD 1000000007;

int main(){
	int n, m;
	cin >> n >> m;
	vector<int> a(m);
	for(int i=0; i<m; i++)
		cin >> a[i];
	vector<long long> dp(n+1);
	dp[n]=1;
	dp[n-1]=1;
	int key=m-1;
	for(int i=n-2; i>=0; i--){
		dp[i] = (dp[i+1]+dp[i+2])%MOD;
		if(key>=0 && i==a[key]){
			dp[i] = 0;
			key--;
		}
	}
	cout << dp[0] << endl;
	return 0;
}