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: Runtime Error)

#include<iostream>
#include<vector>
using namespace std;

int main() {
    int mod = 1000000007;
    int n, m;
    vector<int> broken;
    vector<bool> status(n+1, true);

    cin >> n >> m;
    for (int i = 0; i < m; i++) {
        int tmp;
        cin >> tmp;
        broken.push_back(tmp);
    }

    for (int i = 0; i < m; i++) {
        status[broken[i]] = false;
    }

    int steps = 0;
    int count = 1;
    while (steps < n) {

        if (steps < n-1 && !status[steps+1] && status[steps+2]) {
            count *= 1;
            steps += 2;
        } else if (steps < n-2 && status[steps+1] && !status[steps+2]) {
            count *= 1;
            steps += 3;
        } else if (steps == n-1 && status[steps+1]) {
            count *= 1;
            steps++;
        } else if (status[steps+1] && status[steps+2]){
            count *= 2;
            steps += 2;
        } else {
            count = 0;
            break;
        }
    }
    cout << count % mod << endl;

    return 0;
}