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 <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>

using namespace std;
#define int long long int
const int INF = 1001001001001001LL;
const int MOD = 1000000007;

int di[] = {-1, 0, 1, 0, -1, 1, 1, -1};
int dj[] = {0, 1, 0, -1, 1, 1, -1, -1};

signed main(){
    
    int n, m; cin >> n >> m;
    set<int> s;
    for(int i = 0; i < m; i++){
        int a; cin >> a;
        s.insert(a);
    }
    s.insert(n + 1);

    vector<int> dp(n + 1, 0);
    dp[0] = 1;
    for(int i = 0; i < n; i++){
        if(s.find(i + 1) == s.end()) dp[i + 1] += dp[i];
        dp[i + 1] %= MOD;
        if(s.find(i + 2) == s.end()) dp[i + 2] += dp[i];
        dp[i + 2] %= MOD;
    }
    cout << dp[n] << endl;
    return 0;
}