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;
using System.Text;
using System.Threading.Tasks;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        new Program().Calc();
    }

    Scanner cin;

    public Program() { }

    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    private int[] _dp;

    void Calc()
    {
        cin = new Scanner();

        int N = cin.nextInt();
        int M = cin.nextInt();

        int[] A = cin.ArrayInt(M);



        int[] breakStep = new int[N + 2];


        _dp = new int[N + 1];
        _dp[0] = 1;



        for (int i = 0; i < M; ++i)
        {
            breakStep[A[i]] = 1;
        }

        breakStep[N + 1] = 1;

        for (int i = 1; i <= N; ++i)
        {
            if (breakStep[i] == 1) continue;

            if (i == 1)
            {
                _dp[i] = 1;
            }
            else
            {
                _dp[i] = _dp[i - 1] + _dp[i - 2];
                _dp[i] %= 1000000007;
            }
        }

        WriteLine(_dp[N]);
    }
}

class Modulo
{
    private const int M = 1000000007;
    private readonly int[] m_facs;
    public int Mul(int a, int b)
    {
        return (int)(Math.BigMul(a, b) % M);
    }
    public Modulo(int n)
    {
        m_facs = new int[n + 1];
        m_facs[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
            m_facs[i] = Mul(m_facs[i - 1], i);
        }
    }
    public int Fac(int n)
    {
        return m_facs[n];
    }
    public int Pow(int a, int m)
    {
        switch (m)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, m / 2);
                int p2 = Mul(p1, p1);
                return ((m % 2) == 0) ? p2 : Mul(p2, a);
        }
    }
    public int Div(int a, int b)
    {
        return Mul(a, Pow(b, M - 2));
    }
    public int Ncr(int n, int r)
    {
        if (n < r) { return 0; }
        if (n == r) { return 1; }
        int res = Fac(n);
        res = Div(res, Fac(r));
        res = Div(res, Fac(n - r));
        return res;
    }
}

public static class StringExtension
{
    public static char GetChar1(this string str, int indexOneBase)
    {
        return str[indexOneBase - 1];
    }
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}