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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
namespace C
{
    class Program
    {
        static public int Mod = (int)Math.Pow(10, 9) + 7;
        static void Main(string[] args)
        {
            string[] In = Console.ReadLine().Split(' ');
            int n = int.Parse(In[0]);
            int m = int.Parse(In[1]);
            long[] A = new long[n + 1];
            int[] X = new int[m];
            for (int i = 0; i < m; i++)
            {
                X[i]= int.Parse(Console.ReadLine());
            }
            A[0] = 1;
            int x_inx = 0;
            for (int i = 0; i <= n - 1; i++)
            {
                if (x_inx < m && i == X[x_inx]) { x_inx++; continue; }
                A[i] %= Mod;
                A[i + 1] += A[i];
                if(i!=n-1)A[i + 2] += A[i];
            }
            Console.WriteLine(A[n]%=Mod);
        }
    }
}
//TLE
//namespace C
//{
//    class Program
//    {
//        static public int Mod = (int)Math.Pow(10, 9) + 7;
//        static public bool[] A;
//        static public int n;
//        static public long ans=0;
//        static void Main(string[] args)
//        {
//            string[] In = Console.ReadLine().Split(' ');
//            n = int.Parse(In[0]);
//            int m = int.Parse(In[1]);
//            A = new bool[n+1];
//            A = Enumerable.Repeat(true, n + 1).ToArray();
//            for(int i = 0; i < m; i++)
//            {
//                int a = int.Parse(Console.ReadLine());
//                A[a] = false;
//            }
//            DFS(0);
//            Console.WriteLine(ans);
//        }
//        static public void DFS(int index)
//        {
//            if (index > n) return;
//            if (!A[index]) return;
//            if (index == n) 
//            { 
//                ans++; 
//                ans %= Mod;
//                return; 
//            }
//            DFS(index + 1);
//            DFS(index + 2);
//        }
//    }
//}