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 test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayLong();
            var N = input[0];
            var M = input[1];
            var cnt = new long[N + 1];
            var bro = new bool[N + 1];
            for (int i = 0; i < M; i++) bro[ReadInt()] = true;
            var mod = (long)Math.Pow(10, 9) + 7;
            if (N == 1)
            {
                Console.WriteLine(1);
                return;
            }
            if (!bro[1]) cnt[1]++;
            if (!bro[2]) cnt[2]++;
            for (int i = 1; i < N - 1; i++)
            {
                if (!bro[i])
                {
                    if (!bro[i + 1])
                    {
                        cnt[i + 1] += cnt[i];
                        cnt[i + 1] %= mod;
                    }
                    if (!bro[i + 2])
                    {
                        cnt[i + 2] += cnt[i];
                        cnt[i + 2] %= mod;
                    }
                }
            }
            if (!bro[N - 1])
            {
                cnt[N] += cnt[N - 1];
                cnt[N] %= mod;
            }

            Console.WriteLine(cnt[N]);
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}