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 rep(i, n) for(long long i = 0;i < n;i++)
#define repr(i, n) for(int i = n;i >= 0;i--)
#define Sort(v, n) sort(v, v+n);
#define VSort(v) sort(v.begin(), v.end());
#define ll long long
#define pb(a) push_back(a)
#define INF 999999999
#define cY cout<<"Yes";
#define cN cout<<"No";
#define cA(a) cout<<a;
const ll MOD = 1000000007;



int main() {
    int n,m;
    cin>>n>>m;
    ll p[n+1];
    rep(i,n+1) {
        p[i] = 0;
    }
    p[0] = 1;
    p[1] = 1;
    rep(i,m) {
        int tmp;
        cin >> tmp;
        p[tmp] = -1;
    }
    for(int i = 2;i <= n;i++) {
        if (p[i-2] != -1 && p[i] != -1) p[i] += p[i-2];
        p[i] = p[i]%MOD;
        if (p[i-1] != -1 && p[i] != -1) p[i] += p[i-1];
        p[i] = p[i]%MOD;
    }
    cout << p[n];
}