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;

class Program
{
  static void Main()
  {
    string[] input = Console.ReadLine().Split(' ');
    int N = int.Parse(input[0]);
    int M = int.Parse(input[1]);
    const int mod = 1000000007;
    
    // 壊れている段
    var broken = new Queue<int>();
    for(int i = 0; i < M; i++)
    {
      broken.Enqueue(int.Parse(Console.ReadLine()));
    }
    
    // N段目に到達する場合の数
    int[] dp = new int[N + 5];
    dp[0] = 1;
    
    for (int i = 1; i <= N; i++)
    {
      if (broken.Count != 0 && broken.Peek() == i)
      {
        dp[i] = 0;
        broken.Dequeue();
      }
      else
      {
        if(i == 1)
          dp[1] = 1;
        else
          dp[i] = (dp[i - 2] + dp[i - 1]) % mod;
      }
    }
    
    // 出力
    Console.WriteLine(dp[N]);
    
  }
}