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<vector>
#include<cmath>
#include<string>
#include<algorithm>
#include<map>
#include<utility>
#include<cstdio>

using namespace std;

typedef pair<int,bool> Pair;

int STEP[1000001];
int MEMO[1000001];

int kaidan(int N){

    int ans = 0;

	if(MEMO[N] != -1) return MEMO[N];
	
	if(N==0) return 1;

	if(N < 0) return 0;
	else if(STEP[N]==0)	return 0;
	else if(STEP[N]==1){
	
		ans = (kaidan(N-1) + kaidan(N-2))%1000000007;

	}

	MEMO[N] = ans;
	
	return ans;
	
}

int main(){

  int N,M,ANA;
   
  cin >> N >> M;
   
  for(int i = 0; i <= N; ++i) STEP[i] = 1;
  for(int i = 0; i <= N; ++i) MEMO[i] = -1;
  
  for(int i = 0; i < M; ++i){

    cin >> ANA;
    STEP[ANA] = 0;
	
  }  
  
  cout << kaidan(N);
  
  return 0;

}