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 C___Typical_Stairs
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int n = input[0];
            int m = input[1];

            int[] broken = new int[m];
            int[] dp = new int[n + 1];

            for (int j = 0; j < m; j++)
            {
                broken[j] = int.Parse(Console.ReadLine());
                dp[broken[j]] = -1;
            }

            dp[0] = 1;
            dp[1] = 1;

            if(broken.Contains(1))
            {
                dp[1] = 0;
            }

            for (int i = 2; i < n + 1; i++)
            {
                if (dp[i] == -1) continue;
                if (dp[i - 2] != -1) dp[i] += dp[i - 2];
                if (dp[i - 1] != -1) dp[i] += dp[i - 1];
                dp[i] = dp[i] % 1000000007;
            }

            Console.WriteLine(dp[n]);

        }
    }
}