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;

namespace C___Typical_Stairs
{
    class Program
    {
        static void Main(string[] args)
        {
            var read = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
            var N = read[0];
            var M = read[1];
            var MOD = 1000000007;
            
            var broken = new bool[N+1];
            for(int i = 0 ; i < N+1 ; i++) broken[i] = false;
            for(int i = 0 ; i < M ; i++)
            {
                var A = int.Parse(Console.ReadLine());
                broken[A] = true;
            }      

            var steps = new long[N+1];
            steps[0] = 1;
            steps[1] = broken[1] ? 0 : 1;
            for(int i = 2 ; i < N+1 ; i++)
            {
                if(broken[i])
                {
                    steps[i] = 0;
                }else
                {
                    steps[i] = (steps[i-1]+steps[i-2]) % MOD;
                }
            }

            Console.WriteLine(steps[N]);
        }
    }
}