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;

namespace c
{
    class Program
    {
        static void Main(string[] args)
        {
            var _ = Console.ReadLine().Split();
            var n = int.Parse(_[0]);
            var m = int.Parse(_[1]);

            var a = new bool[1000001];
            for(var i = 0; i < m; i++){
                var t = int.Parse(Console.ReadLine());
                a[t] = true;
            }

            memo[0] = 1;
            memo[1] = 1;
            Console.WriteLine(fib(n, a));
        }

        static long[] memo = new long[1000001];
        static long fib(int n, bool[] a){
            if(a[n]){
                return 0;
            }
            if(memo[n] != 0){
                return memo[n];
            }
            memo[n] = fib(n-1, a) + fib(n-2, a);
            memo[n] %= 1000000007;
            return memo[n];
        }
    }
}