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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.ComponentModel;
using System.Linq;
using System.Threading.Tasks;
class Program
{
	static void Main(string[] args)
	{
		
		var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
		int N = input[0];
		int M = input[1];
        
		List<int> a = new List<int>();
		bool ok = true;
		long ans = 0;
		if (M > 0)
		{
			for (var i = 0; i < M; i++)
			{
				a.Add(int.Parse(Console.ReadLine()));
				if (i >= 1 && a[i] - a[i - 1] == 1)
				{
					ok = false;
					break;
				}
			}
		}
		else { ok = false; }

		long[] path = new long[100007];
		path[0] = 0;
		path[1] = 1;
		path[2] = 1;
        for(var i = 3; i < 100007; i++)
		{
			path[i] = path[i - 1] + path[i - 2];
		}
		

		if (ok)
		{
			ans = path[a[0]];
			if (M > 1)
			{
				for (var i = 1; i < M; i++)
				{
					ans = (ans * path[a[i] - a[i - 1] - 1]) % 1000000007;
				}
			}
			ans = (ans * path[N - a[M - 1]])% 1000000007;
		}
		if (M == 0)
		{
			ans = path[N + 1];
		}

		Console.WriteLine(ans);






	}
}