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;
using System.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = l[0], M = l[1];

            var broke = new long[M];
            for (var i = 0; i < M; i++)
            {
                broke[i] = long.Parse(Console.ReadLine());
            }

            // 例外ケースをはじいておく
            for (var i = 1; i < M; i++)
            {
                if (broke[i] - broke[i-1] == 1)
                {
                    Console.WriteLine(0);
                    return;
                }
            }

            var df = new DfsMaster(N);
            var total = 1L;
            for (var i = 0; i < M; i++)
            {
                if (i == 0)
                {
                    total *= df.Fib(broke[i]);
                    continue;
                }
                total *= df.Fib(broke[i] - broke[i - 1] - 1);
            }
            total *= df.Fib(N - broke[M - 1]);

            Console.WriteLine(total % 1000000007);

        }
    }
    public class DfsMaster
    {
        public long[] Memo { get; set; }

        public DfsMaster(long x)
        {
            Memo = new long[x];
        }

        public long Fib(long n)
        {
            if (n == 0) return 0;
            if (n == 1) return 1;
            if (Memo[n] != 0) return Memo[n];

            return Memo[n] = Fib(n - 1) + Fib(n - 2);

        }
    }
}