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>
typedef long long ll;
using namespace std;
int a[100001];
int Count = 0;
int fib[100001];

int fibonacci(int n) {
    int i;
    fib[0] = 1;
    if(a[Count] == 1){
        fib[1] = 0;
        Count++;
    }
    else fib[1] = 1;
    for(i = 2; i <= n; ++i) {
        if(i == a[Count]){
            fib[i] = 0;
            Count++;
        }
        else{
            fib[i] = (fib[i-1] + fib[i-2])%1000000007;
        }

    }
    return fib[n];
}

int main(){
    int N,M;
    cin >> N >> M;
    for (int i = 0; i < M; i++)
    {
        cin >> a[i];
    }
    int ans = fibonacci(N);
    cout << ans << endl;
}