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

unsigned long long step(long num);

int main(void){
	unsigned long long N,M;
	std::cin>>N>>M;
	std::vector<unsigned long long> steps;

	unsigned long long first = 1;	
	for(unsigned long long i=0;i<M;i++){
		unsigned long long a;
		std::cin>>a;
		long long tmp = a - first;	
			if(tmp < 0){
				std::cout<<"0"<<std::endl;
					return 0;
			}
		steps.push_back(tmp);
		first = a + 2;
		if(i == M-1){
			long long tmp = N - a - 1;
			if(tmp <= 0){
				tmp = 1;
		}
	steps.push_back(tmp);
		}
	}

	unsigned long long ans = 1;
	for(auto sptr = steps.begin();sptr != steps.end();sptr++){
		if(*sptr == 0){
			if(sptr == steps.begin()){
				*sptr = 1;
			}else{
				std::cout<<0<<std::endl;
				return 0;
			}
		}
		ans = ans * step(*sptr);
//		std::cout<< *sptr << "    " <<ans << std::endl;
	}

	ans = ans % 1000000007;

	std::cout<<ans<<std::endl;

	return 0;
}

unsigned long long step(long num){
	unsigned long long f1 = 0;
	unsigned long long f0 = 1;
	unsigned long long ans = 0;

	if(num == 0){
		return 0;
	}

	for(unsigned long long i=0;i<num + 1;i++){
		ans = (f1 + f0) % 1000000007;	
		f0 = f1 % 1000000007;
		f1 = ans % 100000007;
	}

	return ans;
}