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;

unsigned long fib(int x) {
  int a = 1;
  int b = 1;
  int c = 0;
  for(int i = 1;i < x;i++){
    c = b;
    b = a + b;
    a = c;
  }
  return b;
}

  
int main(){
  unsigned long MOD = 1000000007;
  int N, M;
  cin >> N >> M;
  vector<int> a(M);
  for(int i = 0;i < M;i++){
    cin >> a[i];
  }
  unsigned long ans = fib(a[0] - 1) % MOD;
  bool check = true;
  for(int i = 0;i < M - 1;i++){
    if(a[i] + 1 == a[i + 1]){
      cout << 0;
      check = false;
      break;
    }
    cout << (fib(a[i + 1] - a[i] - 1));
    ans = ((ans % MOD) * (fib(a[i + 1] - a[i] - 2) % MOD)) % MOD;
  }
  if(check){
    cout << fib(N - a[M - 1] - 1);
    cout << ((ans % MOD) * (fib(N - a[M - 1] - 1) % MOD)) % MOD;
  }
}