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<iostream>
using namespace std;
long long hoge = 1000000007;

int main(){
  int n, m, head = 0;
  // 標準入力
  cin >> n >> m;

  int a[m+1];
  long long s[n+1];
  for ( int i = 0; i < m; i++){ cin >> a[i];}
  a[m] = 0;
  a[m+1] = 0;

  // init
  for ( int i = 0; i <= n; i++){ s[i] = 0;}

  // 1段目
  s[0] = 1;
  s[1] = 1;
  // 2段目から始める
  for ( int i = 2; i <= n; i++){
//    cout << "i-2: " << i-2 << " i-1: " << i-1 <<  endl;
//    cout << a[head]  << ", "<< a[head+1] << endl;
    if (i-2 == a[head] && i-1 == a[head+1]){
      s[i] = 0;
      break;
    } else if (i-2 == a[head] && i-1 != a[head+1]){
      s[i] = s[i-1];
      head++;
//      cout << "a" << endl;
    } else if (i-2 != a[head] && i-1 == a[head]){
      s[i] = s[i-2];
//     cout << "b" << endl;
    } else {
      s[i] = s[i-2] + s[i-1];
//    cout << "c" << endl;
    }

//   cout << "s[i]: " << s[i] << endl;
//   cout << "-----------------" << endl;
//
//   cout << "a[" << head <<"]" << ": " << a[head] << endl;
//   cout << "a[" << head+1 <<"]" << ": " << a[head+1] << endl;
//   cout << "s[" << i << "]" << ": " << s[i] << endl;

   s[i] = s[i]%hoge;
  }

  cout << s[n]%hoge << endl;

  return 0;
}