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.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])%1000000007;
		}
		

		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] % 1000000007;
		}

		Console.WriteLine(ans);






	}
}

//var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
//入力用

public class Calculation //各種値の計算メソッド
{
    public int GetGcd(int a, int b) //最大公約数(２数)
	{
		if (a * b == 0)
		{
			return 0;
		}
		if (a < b)
		{
			int c = a;
			a = b;
			b = c;
		}

		int r = a % b;
		while (r > 0)
		{
			a = b;
			b = r;
			r = a % b;
		}
		return b;
	}
	public int GetGcdOfSortedArray(int[] array) //最大公約数(ソート済み数列)
	{
		if (array.Length == 0) { return 1; }
		else if (array.Length == 1) { return array[0]; }
		else
		{
			int n = 0;
			int g = -1;
			while (n <= array.Length - 2)
			{
                
				int a = array[n + 1];
				int b = array[n];
				int r = a % b;
				while (r > 0)
				{
					a = b;
					b = r;
					r = a % b;
				}
				g = b;
				array[n + 1] = g;
				n++;
			}

			return g;

		}
	}
	public long GetGcdOfSortedArrayL(long[] array) //最大公約数(ソート済み配列[long型])
	{
		if (array.Length == 0) { return 1; }
		else if (array.Length == 1) { return array[0]; }
		else
		{
			int n = 0;
			long g = -1;
			while (n <= array.Length - 2)
			{

				long a = array[n + 1];
				long b = array[n];
				long r = a % b;
				while (r > 0)
				{
					a = b;
					b = r;
					r = a % b;
				}
				g = b;
				array[n + 1] = g;
				n++;
			}

			return g;

		}
	}

	public long GetNCR(int n, int r) //二項係数(生の値)
	{
		if (n == 1) { return 1; }
		long[] nC = new long[n + 1];
		nC[0] = 1;
		for (var i = 0; i <= r - 1; i++)
		{
			nC[i + 1] = nC[i] * (n - i) / (i + 1);
		}
		return nC[r];
	}


}

class Modulo //1000000007で割る問題用
{
	private const int M = 1000000007;
	private readonly int[] m_facs;
	public int Mul(int a, int b) //掛け算
	{
		return (int)(Math.BigMul(a, b) % M);
	}
	public Modulo(int n)
	{
		m_facs = new int[n + 1];
		m_facs[0] = 1;
		for (int i = 1; i <= n; ++i)
		{
			m_facs[i] = Mul(m_facs[i - 1], i);
		}
	}
	public int Fac(int n)
	{
		return m_facs[n];
	}
	public int Pow(int a, int m)　//累乗
	{
		switch (m)
		{
			case 0:
				return 1;
			case 1:
				return a;
			default:
				int p1 = Pow(a, m / 2);
				int p2 = Mul(p1, p1);
				return ((m % 2) == 0) ? p2 : Mul(p2, a);
		}
	}
	public int Div(int a, int b)　//除算
	{
		return Mul(a, Pow(b, M - 2));
	}
	public int Ncr(int n, int r)　//二項係数
	{
		if (n < r) { return 0; }
		if (n == r) { return 1; }
		int res = Fac(n);
		res = Div(res, Fac(r));
		res = Div(res, Fac(n - r));
		return res;
	}
	public Modulo() { }
}