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;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading;
using System.Threading.Tasks;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var N = NM[0]+1;
            var M = NM[1];
            var am = new HashSet<int>();
            for (var i=0;i<M;i++)
            {
                am.Add(int.Parse(Console.ReadLine()));
            }
            var dp = new List<int>(Enumerable.Range(0,N).Select(s=>0));
            dp[0] = 1;
            if (am.Contains(0)) dp[0] = 0;

            for (var i=1;i<N;i++)
            {
                if (am.Contains(i)) continue;
                else dp[i] = dp[i - 1];
                if (1 < i)
                {
                    dp[i] += dp[i - 2];
                    dp[i] %= 1000000007;
                }
            }
            Console.WriteLine(dp[N-1]);
        }
    }
}