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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;

class Solve {
    static void Main(string[] args) {
        var arr = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = arr[0], M = arr[1];
        var set = new HashSet<int>();
        for (int i = 0; i < M; i++) {
            set.Add(int.Parse(Console.ReadLine()));
        }
        var dp = new long[N + 1];
        dp[0] = 1;
        if (N >= 1) {
            dp[1] = set.Contains(1) ? 0 : 1;
            for (int i = 2; i <= N; i++) {
                if (set.Contains(i)) continue;
                var a = set.Contains(i - 1);
                var b = set.Contains(i - 2);
                dp[i] = a && b ? 0 :
                        a ? dp[i - 2] : 
                        b ? dp[i - 1] : (dp[i - 1] + dp[i - 2]) % 1000000007;
            }   
        }
        var answer = dp[^1];
        var writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(writer);
        Console.WriteLine(answer);
        Console.Out.Flush();
    }
}