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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class AtCoderC
{
    private static int n;
    private static int m;
    private static int[] broken;
    private static long[] patterns;
    private static long mod = 1000000007;
    static void Main()
    {
        {
            string line = Console.ReadLine();
            var words = line.Split(' ');
            n = int.Parse(words[0]);
            m = int.Parse(words[1]);
        }

        broken = new int[m];
        {
            for (int i = 0; i < m; i++)
            {
                broken[i] = int.Parse(Console.ReadLine());
            }
        }

        patterns = new long[n + 1];
        patterns[0] = 1;
        patterns[1] = broken.Contains(1) ? 0 : 1;
        long answer = Solve(n);
        Console.WriteLine(answer);
    }

    private static long Solve(int n)
    {
        if (broken.Contains(n))
        {
            patterns[n] = 0;
            return 0;
        }
        if (patterns[n] != 0)
        {
            return patterns[n];
        }
        long pattern = (Solve(n - 1) + Solve(n - 2)) % mod;
        patterns[n] = pattern;
        return pattern;
    }
}