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.Linq;
using System.Collections.Generic;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var a = new int[nm[1]];
            var isStepAble = new bool[nm[0] + 1];

            int MOD = 1000000007;

            a = a.Select(x => x = int.Parse(Console.ReadLine())).ToArray();

            for (int i = 0; i < isStepAble.Count(); i++)
            {
                isStepAble[i] = true;
            }

            foreach (var x in a)
            {
                isStepAble[x] = false;
            }

            var dp = new int[nm[0] + 1];

            dp[0] = 1;
            dp[1] = isStepAble[1] ? 1 : 0;
            // dp[2] = isStepAble[2] ? dp[1] == 1 ? 2 : 1 : 0;

            for (int i = 2; i < dp.Count(); i++)
            {
                dp[i] = ((dp[i - 1] + dp[i - 2]) % MOD) * (isStepAble[i] ? 1 : 0);
            }
            Console.WriteLine(dp.Last());

        }
    }
}