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 <iostream>
#include <iomanip>
#include <cstdio>
#include <queue>
#include <cstring>
#include <vector>
#include <map>
#include <algorithm>
#include <cctype>
#include <cmath>
#include <bitset>
#include <set>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define RREP(i,n) for(int i=n-1;i>=0;i--)
#define FOR(i,k,n) for(int i=(k);i<(int)(n);i++)
#define all(i,n) (i),(i+n)

int dx4[4]={1,0,-1,0};
int dy4[4]={0,-1,0,1};
int dx8[8]={1,0,-1,1,-1,1,0,-1};
int dy8[8]={1,1,1,0,0,-1,-1,-1};

typedef pair<int, int> P;
typedef pair<string, int> SP;
typedef long long ll;

const int INF = 1e9;
const ll LLINF = 1e18;
const int MAX_V = 1e6+1;
const ll mod = 1000000007;

// --------------------------------------
int n, m;
vector<int> v;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> n >> m;
  vector<bool> v(n + 1, true);
  REP(i, m) {
    int a;
    cin >> a;
    v[a] = false;
  }

  vector<int> memo(n + 1, 0);
  memo[0] = 1;
  FOR(i, 1, n + 1) {
    if(v[i]) {
      if(i == 1) memo[i] = memo[i - 1] % mod;
      else memo[i] = (memo[i - 1] + memo[i - 2]) % mod;
    } else {
      memo[i] = 0;
    }
  }

  cout << memo[n] << endl;
}