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.Collections.Generic;
using System.Linq;

namespace ABC129C
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] NM = CIN.LongArray();
            long[] A = new long[NM[1]];
            for (int i = 0; i < NM[1]; i++)
            {
                A[i] = CIN.Long();
            }

            Dictionary<long, bool> AI = new Dictionary<long, bool>();
            foreach (long l in A)
            {
                if (AI.ContainsKey(l))
                {
                    continue;
                }
                AI.Add(l, true);
            }

            long[] dp = new long[NM[0] + 1];
            dp[0] = 1;
            for (int i = 1; i <= NM[0]; i++)
            {
                if (AI.ContainsKey(i))
                {
                    dp[i] = 0;
                    continue;
                }

                dp[i] = dp[i - 1];
                if (i > 1)
                {
                    dp[i] = (dp[i] + dp[i - 2]) % 1000000007;
                }
            }

            Console.WriteLine(dp[NM[0]]);
        }
    }

    internal static class CIN
    {
        public static string String()
        {
            return Console.ReadLine();
        }

        public static int Int()
        {
            return int.Parse(Console.ReadLine());
        }

        public static int[] IntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        public static long Long()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] LongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] DoubleArray()
        {
            return Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
        }
    }
}