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.Text.RegularExpressions;

namespace kp
{
    public class Program
    {
        //static long[,] cmb;
        static int MAX_INT = 1000000007;
        static void Main(string[] args)
        {
            //int N = Int32.Parse(Console.ReadLine());
            int[] input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
            int N = input[0];
            int M = input[1];

            HashSet<int> stair = new HashSet<int>();
            for(int i=0; i<M; i++)
            {
                int a = Int32.Parse(Console.ReadLine());
                stair.Add(a);
            }

            long[] dp = new long[N+1]; // i段目にたどり着く方法は何通り？
            dp[0] = 1;
            if (stair.Contains(1))
                dp[1] = 0;
            else
                dp[1] = 1;
            #region DP
            for (int i = 2; i <= N; i++ )
            {
                // i段目が壊れていたら0
                if(stair.Contains(i))
                {
                    dp[i] = 0;
                }
                else
                {
                    dp[i] = dp[i - 1] + dp[i - 2];
                    dp[i] %= MAX_INT;
                }
            }
                
            #endregion DP
            Console.WriteLine(dp[N] + "");


        }
    }
}