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.Generic;
using System.Linq;
using System.Numerics;


namespace AtCoderWorkspace
{
    class Program
    {
        static void Main(string[] args)
        {
            var cin = new Scanner();
            var N = cin.nextInt();
            var M = cin.nextInt();
            ulong mod = 1000000007;


            int[] a = new int[M];
            for(int i = 0; i<M; i++)
            {
                a[i] = cin.nextInt();
            }

            // 無理判定
            var before = -9;
            for(int i = 1; i<a.Length; i++)
            {
                if(before == a[i] - 1)
                {
                    Console.WriteLine(0);
                    return;
                }
                before = a[i];
            }            
            
            var dp = new ulong[N + 1];
            if (a[0] == 1)
            {
                dp[0] = 1;
                dp[1] = 0;
            }
            else
            {
                dp[0] = 1;
                dp[1] = 1;
            }            

            for(int i = 2; i <= N; i++)
            {
                if (BinarySearch(a,i) != -1)
                {
                    dp[i] = 0;
                }
                else
                {
                    // 通常
                    if(dp[i-1] == 0)
                    {
                        dp[i] = dp[i - 2];
                        continue;
                    }
                    if(dp[i-2] == 0)
                    {
                        dp[i] = dp[i - 1];
                        continue;
                    }
                    dp[i] = (dp[i - 1] + dp[i - 2]) % mod;
                }                
            }

            Console.WriteLine(dp[N]);
        }

        public static int BinarySearch<T>(T[] array, T target) where T : IComparable<T>
        {
            int min = 0;
            int max = array.Length - 1;

            while (true)
            {
                if (max < min) return -1;
                int mid = min + (max - min) / 2;
                switch (target.CompareTo(array[mid]))
                {
                    case -1:    
                        max = mid - 1;
                        break;
                    case 1:     
                        min = mid + 1;
                        break;
                    case 0:     
                        return mid;
                }
            }
        }
    }

    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;
        }
    }
}