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;

int Fibonacci(long long n) {
  int y=1;
  int x=1;
  for (int i=0;i<n-1;i++){
  int p=x;
   x=y;
    y=x+p;
  }
   return y;
}
int main() {
  long long N;
  long long M;
  cin >>N>>M;
  if (M==0){
    long long c= Fibonacci(N)%1000000007;
    cout <<c <<endl;
  }
  
  else{
  vector<long long>data(M);
  for (long long i=0;i<M;i++){
    cin >>data.at(i);
  }
  long long  p= data.at(0)-1;
  long long s =Fibonacci(p);
  
  for (long long i=0;i<M-1;i++){
   long long e= data.at(i+1)-data.at(i)-2;
   if (e<0){
   s*=0;     
   }
   else {
     s*=Fibonacci(e);
     cout <<s<<endl;
   }
  }  
  long long r=N-data.at(M-1)-1;
  s*=Fibonacci(r);
  
  s%= 1000000007;
 
  cout << s<<endl;
  }
}