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: Accepted)

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

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("6 1");
            WillReturn.Add("3");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("10 2");
            WillReturn.Add("4");
            WillReturn.Add("5");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("100 5");
            WillReturn.Add("1");
            WillReturn.Add("23");
            WillReturn.Add("45");
            WillReturn.Add("67");
            WillReturn.Add("89");
            //608200469
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = InputList[0].Split(' ').Select(X => int.Parse(X)).ToArray();
        int N = wkArr[0];

        var ASet = new HashSet<int>();
        foreach (string EachStr in InputList.Skip(1)) {
            ASet.Add(int.Parse(EachStr));
        }

        //場合の数[現在位置]なDP表
        int[] DPArr = new int[N + 1];
        DPArr[0] = 1;
        int UB = N;

        for (int I = 0; I <= UB; I++) {
            int NextDan;

            //1段あがる場合
            NextDan = I + 1;
            if (NextDan <= UB && ASet.Contains(NextDan) == false) {
                DPArr[NextDan] = DPArr[NextDan] + DPArr[I];
                DPArr[NextDan] %= 1000000007;
            }

            //2段あがる場合
            NextDan = I + 2;
            if (NextDan <= UB && ASet.Contains(NextDan) == false) {
                DPArr[NextDan] = DPArr[NextDan] + DPArr[I];
                DPArr[NextDan] %= 1000000007;
            }
        }
        Console.WriteLine(DPArr[UB]);
    }
}