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;
using System.Text;
using System.Threading.Tasks;

namespace ABC129_C
{
    class Program
    {
        static long[] fibo = new long[100001];
        static long mod = 1000000007;
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var a = new int[NM[1]];
            var imp = false;
            for (int i = 0; i < NM[1]; i++)
            {
                a[i] = int.Parse(Console.ReadLine());
                if (i > 0 && a[i] - a[i - 1] == 1)
                {
                    imp = true;
                }
            }

            if (imp)
            {
                Console.WriteLine(0);
            }
            else
            {
                long ans = 0;
                var temp = 0;
                foreach (var i in a)
                {
                    if (ans == 0)
                    {
                        ans += CalcFibo(i - 1 - temp);
                    }
                    else
                        ans *= CalcFibo(i - 1 - temp);
                    ans %= mod;

                    temp = i + 1;
                }

                if (ans == 0)
                {
                    ans += CalcFibo(NM[0] - temp);
                }
                else
                    ans *= CalcFibo(NM[0] - temp);
                ans %= mod;

                Console.WriteLine(ans);
            }
        }

        static long CalcFibo(int n)
        {
            if (n <= 1) return 1;
            if (fibo[n] != 0) return fibo[n];
            fibo[n] = (CalcFibo(n - 1) + CalcFibo(n - 2))%mod;

            return fibo[n];
        }
    }
}