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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
public class ABC
{
    public static int[] steps;

    public static void Main()
    {
        var W = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int N, M;
        N = W[0];
        M = W[1];
        steps = new int[N + 1];
        int[] a = new int[M];
        for (int i = 0; i < M; i++)
        {
            a[i] = int.Parse(Console.ReadLine());
        }

        Console.WriteLine(step_count(N, a));

    }

    public static long step_count(int step, int[] broken)
    {

        if (steps[step] != 0) return steps[step];
        if (step == 0) return 1;
        if (step < 0) return 0;

        if (broken.Contains(step)) return 0;
        else
        {
            long check_over = step_count(step - 1, broken) + step_count(step - 2, broken);
            if (check_over > 100000007) check_over -= 100000007;
            steps[step] = (int)check_over;
            return check_over;
        }
    }

}