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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

long long fib(long long s){
	if(s<2)
	{
		return 1;
	}
	else if(s==2)
	{
		return 2;
	}
	else
	{
		long long a=1,b=2,r=1;
		for(int i=2;i<s;i++)
		{
			r=a+b;
			a=b;
			b=r;
		}
		r%=1000000007;
		return r;
	}
}

int main() {
	long long n,m;
	cin >> n >> m;
	vector<long long> a(m);
	for(int i=0;i<m;i++)
	{
		cin >> a.at(i);
	}
	long long ans=1,c=-1;
	for(int i=0;i<m;i++)
	{
		if(i<m-1)
		{
			if(a.at(i)==a.at(i+1)-1)
			{
				ans=0;
				break;
			}
		}
		if(a.at(i)==1)
		{
			if(m==1)
			{
				ans=0;
				break;
			}
			c=1;
			continue;
		}
		long long s=a.at(i)-c-2;
		c=a.at(i);
		ans=(ans*fib(s))%1000000007;
		if(i==m-1)
		{
			s=n-c-1;
			ans=(ans*fib(s))%1000000007;
		}
	}
	cout << ans << endl;
	return 0;
}