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.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramC
    {
        static void Main(string[] args)
        {
            var mod = (int)1e9 + 7;
            var inputs = Console.ReadLine().Split(" ");
            var n = int.Parse(inputs[0]);
            var m = int.Parse(inputs[1]);

            var ok = new bool[n + 1];
            for (var i = 0; i < n + 1; i++)
            {
                ok[i] = true;
            }

            for (var i = 0; i < m; i++)
            {
                var a = int.Parse(Console.ReadLine());
                ok[a] = false;
            }

            var dp = new int[n + 1];
            dp[0] = 1;
            for (var i = 0; i < n; i++)
            {
                for (var j = i + 1; j <= Math.Min(n, i + 2); j++)
                {
                    if (ok[j])
                    {
                        dp[j] += dp[i];
                        dp[j] %= mod;
                    }
                }
            }

            Console.WriteLine(dp[n]);
        }
    }
}