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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;

int main(){
  ll MOD = 1000000007;
  ll n,m;
  cin >> n >> m;
  vector<ll> a(m+2);
  a[m+1] = n+1, a[0] = -1;
  rep(i,m) cin >> a[i+1];
  rep(i,m){
    if(a[i] + 1 == a[i+1]){
      cout << 0 << endl;
      return 0;
    }
  }
  vector<ll> b(n+1);
  b[1] = 1, b[2] = 2;
  for(ll i=3; i<=n; i++){
    b[i] = (b[i-1] + b[i-2]) % MOD;
  }
  ll ans = 1;
  rep(i,m+1){
    if(a[i+1] == 1 || a[i] == n-1 || a[i+1] - a[i] -2 == 0) continue;
    else{
      ans *= b[a[i+1] - a[i] -2];
      ans %= MOD;
      //cout << a[i+1] - a[i] -2 << endl;
    }
  }
  cout << ans << endl;
}