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 <vector>
#include <string>
#include <algorithm>
using namespace std;
vector<int> a;
vector<bool> isok;
int mod = 1000000007;
int main(void){
    int n,m;
    cin >> n >> m;
    a.resize(m);
    isok.assign(n+1,true);
    for(int i = 0;i < m;i++){
        cin >> a[i];
        isok[a[i]] = false;
    }
    
    vector<int> dp(100010);
    dp[0] = 1;
    if(isok[1]) dp[1] = 1;
    
    for(int i = 2;i <= n;i++){
        if(isok[i-2]){
            dp[i] += dp[i-2];
            dp[i] %= mod;
        }
        if(isok[i-1]){
            dp[i] += dp[i-1];
            dp[i] %= mod;
        }
    }
    cout << dp[n] << endl;
    return 0;
}