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: Runtime Error)

using System;

namespace AtCoderABC129C
{
    class Program
    {
        static void Main(string[] args)
        {
            int MOD = 1000000007;
            long ans = 1;

            string[] s = Console.ReadLine().Split(' ');

            int N = int.Parse(s[0]);
            int M = int.Parse(s[1]);

            int[] X = new int[M + 1];
            int[] A = new int[M + 1];

            int F = int.Parse(Console.ReadLine());

            X[0] = F;

            for (int i = 1; i < M; i++)
            {
                int T = int.Parse(Console.ReadLine());
                X[i] = T - F - 1;
                F = T;
            }

            X[M] = N - F;

            Array.Sort(X);

            if(X[0] == 0)
            {
                Console.WriteLine("0");
                return;
            }

            int V1 = 0;
            int V2 = 1;
            int index = 1;

            for(int i=0;i<M+1;i++)
            {
                while(X[i] != index)
                {
                    int temp = (V1 + V2) % MOD;
                    V1 = V2;
                    V2 = temp;

                    index++;
                }

                A[i] = V2;
            }

            for (int i = 0; i < M+1;i++)
            {
                ans = (ans * A[i]) % MOD;
            }

            Console.WriteLine(ans.ToString());
        }
    }
}