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 AtCoder
{
    class Program
    {
        static int MODBASE = 1000000007;
        static void Main(string[] args)
        {
            int[] nm = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
            int n = nm[0];
            int m = nm[1];
            int[] memos = new int[n + 1];
            memos = memos.Select(v => -1).ToArray();
            memos[0] = 1;
            int[] traps = new int[n + 1];
            for (int i = 0; i < m; i++)
            {
                traps[int.Parse(Console.ReadLine())] = 1;
            }

            Console.WriteLine(wayCount(n, ref memos, ref traps).ToString());
        }

        static int wayCount(int step, ref int[] memos, ref int[] traps)
        {
            if (step < 0) return 0;
            if (memos[step] >= 0) return memos[step];
            if (traps[step] == 1) return 0;
            memos[step] = (wayCount(step - 1, ref memos, ref traps) + wayCount(step - 2, ref memos, ref traps)) % MODBASE;
            return memos[step];
        }
    }
}