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;

public class Program {
    public static void Main() {
        var arr = Console.ReadLine().Split(' ').Select(t => int.Parse(t)).ToArray();
        var n = arr[0];
        var m = arr[1];

        var init = new Dictionary<int, long>();
        bool isContain1 = false;
        bool isContain2 = false;

        for (int i = 0; i < m; i++) {
            var digit = int.Parse(Console.ReadLine());
            init.Add(digit, 0);
            if (digit == 1) {
                isContain1 = true;
            } else if (digit == 2) {
                isContain2 = true;
            }
        }

        long score = Route(n, isContain1, isContain2, init) % 1000000007;
        Console.WriteLine(score);
    }

    static long Route(int step, bool isContain1, bool isContain2, Dictionary<int, long> memo) {
        if (step <= 0) {
            return 0;
        }

        long ret;
        if (memo.TryGetValue(step, out ret)) {
            return ret;
        }

        if (step == 1) {
            memo.Add(1, 1);
            return 1;
        }

        if (step == 2) {
            if (isContain1) {
                memo.Add(2, 1);
                return 1;
            }

            memo.Add(2, 2);
            return 2;
        }

        var stairMinus2 = Route(step - 2, isContain1, isContain2, memo);
        var stairMinus1 = Route(step - 1, isContain1, isContain2, memo);
        
        ret = stairMinus1 + stairMinus2;
        memo.Add(step, ret);

        return ret;
    }
}