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;

namespace AtcoderProgram
{

    class Program
    {
        static Dictionary<int, int> fib = new Dictionary<int, int>();

        static void createfib(int n)
        {
            fib.Add(0, 1);
            fib.Add(1, 1);
            fib.Add(2, 2);
            for(int i=3; i<n;i++)
            {
                int a, b;
                fib.TryGetValue(i - 1, out a);
                fib.TryGetValue(i - 2, out b);
                fib.Add(i, a + b);
            }
        }

        static void Main(string[] args)
        {
            string[] nm = Console.ReadLine().Split(' ');
            int num = int.Parse(nm[0]);
            int m = int.Parse(nm[1]);


            if (num == 1)
            {
                Console.WriteLine(1);
                return;
            }
            if (num == 2)
            {
                Console.WriteLine(m == 0 ? 2 : 1);
                return;
            }

            createfib(num);
            if (m == 0)
            {
                int fff;
                fib.TryGetValue(num, out fff); 
                Console.WriteLine(fff);

            }

            int[] elm = new int[m];
            for(int i=0; i<m; i++)
            {
                elm[i] = int.Parse(Console.ReadLine());
            }
            
            List<int> prod = new List<int>();
            for (int i = 0; i < elm.Length; i++)
            {
                if (i == 0) prod.Add(elm[i]-1);
                else
                {
                    if (elm[i] - elm[i - 1] == 1)
                    {
                        Console.WriteLine(0);
                        return;
                    }
                    prod.Add(elm[i] - elm[i - 1] - 2);
                }
            }
            prod.Add(num - elm[m-1] - 1);

            Int64 res = 1;
            foreach(int j in prod)
            {
                int k;
                fib.TryGetValue(j, out k);
                Console.WriteLine(k);
                res = res * k;
                res = res % 1000000007;
            }

            Console.WriteLine(res);
        }
    }
}