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: Accepted)

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

#define el '\n'
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define DEBUG cerr << "DEBUG >>> " 
#define ms(a,b) memset(a, b, sizeof(a))

typedef long long ll;

const int nax = 1e5+5;
const int mod = 1e9+7;
int dp[nax];
bool cant[nax];

int main(){
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cerr.tie(0);

  int n, m;
  cin >> n >> m;
  for(int i = 0; i < m; i++){
    int x;
    cin >> x;
    cant[x] = 1;
  }
  dp[0] = 1;
  for(int i = 1; i <= n; i++){
    if(!cant[i]) dp[i] += (dp[i-1]+dp[i-2])%mod;
    else dp[i] = 0;
  }
  cout << dp[n] << el;

  return 0;
}