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.Collections.Generic;
using System.Linq;

namespace ConsoleApp
{
    class Program
    {
        static int[] a;

        static void Main(string[] args)
        {
            var ss = Console.ReadLine().Split();
            var N = int.Parse(ss[0]);
            var M = int.Parse(ss[1]);

            a = new int[M];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = int.Parse(Console.ReadLine());
            }

            var num = new long?[N + 2];
            var number = BTree(0, N, num);

            Console.WriteLine(number % 1000000007);
        }

        static long? BTree(int current, int goal, long?[] num)
        {
            if (num[current] != null) return num[current];

            if (a.Contains(current) || current > goal)
            {
                return 0;
            }

            if (current == goal)
            {
                return 1;
            }

            var add1 = (current + 1 > goal) ? 0L : BTree(current + 1, goal, num);
            var add2 = (current + 2 > goal) ? 0L : BTree(current + 2, goal, num);

            num[current] = add1 + add2;
            return num[current];
        }
    }
}