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 <cmath>
#include <limits>
#include <iostream>
using namespace std;


int main(){
int n,m;
int point=0;
cin >> n >> m;
const long MOD=1000000007;
int a[100010];
long long int dp[100000]={};
for(int i=0;i<m;i++){
  cin >>a[i];
}
a[m]=-1;
dp[0]=1;
dp[1]=1;
dp[2]=2;
for (int i = 0; i <= n; i++)
{
  if(i==a[point]){
    dp[i]=0;
    point++;
  }else if(i!=0 and i!=1){
    dp[i]=dp[i-1]+dp[i-2];
    dp[i]%=MOD;
  }


}
cout <<dp[n]<<endl;
}