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: Runtime Error)

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

int main(){
  int N, M;
  cin >>N>>M;
  vector<int> A(M);
  for (int i=0;i<M;i++)cin >> A[i];
  A.push_back(N+1);

  
  vector<long long> memo(N);
  int i = 0;
  while (i<=N+1){
    if(i==0) memo[0] = 0;
    if(i==1) memo[1] = 1;
    if(i>1) memo[i] = memo[i-1] + memo[i-2];
    i++;
  }
  
  long long ans = 1;
  
  int dist = A[0];
  //cout << dist << memo[dist] << endl; //test
  ans *= memo[dist];
  ans %= 1000000007;
  
  for (int i=0;i<M;i++){
    dist = A[i+1] - A[i] - 1;
    //cout << memo[dist] << endl; //test
    ans *= memo[dist];
    ans %= 1000000007;
  }
  
  cout << ans << endl;
}