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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Mondai
{
    static void Main()
    {
        var waru= 1000000007;
        var nm = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var N = nm[0];
        var M = nm[1];
        var a = new int[M];
        for (int i=0;i<M;++i) a[i] = Int32.Parse(Console.ReadLine());
        var dp = new int[N + 1];
        dp[0] = 1;
        for (int i=1;i<=N;++i)
        {
            if (a.Contains(i)) continue;
            dp[i] = (dp[i]+dp[i - 1])% waru;
            if(2<=i)dp[i] = (dp[i]+dp[i - 2])% waru;
        }
        Console.WriteLine(dp[N]);
    }
}