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: Runtime Error)

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

namespace agc030_a
{
    class Program
    {
        static void Main(string[] args)
        {
            var text = Console.ReadLine();
            var list = text.Split(' ').Select(x => int.Parse(x)).ToList();

            var n = list[0];
            var b = list[1];

            var blocks = new List<int>();
            for(int i = 0; i < b; i++){
                text = Console.ReadLine();
                blocks.Add(int.Parse(text));
            }

            blocks = blocks.OrderBy(x => x).ToList();
            for(int i = 1; i < blocks.Count; i++){
                if (blocks[i -1] == blocks[i] + 1){
                    Console.WriteLine("0");
                    return;
                }
            }

            var value = 0;
            if (blocks.Count == 0){
                var pow = blocks.Count / 2;
                var mod = blocks.Count % 2;
                value = Convert.ToInt32(Math.Pow(2, pow)) + mod;
            }
            else
            {
                var start = 0;
                for(int i = 0; i < blocks.Count; i++){
                    var point = blocks[i] - 1;
                    var stair = point - start;
                    var pow = stair / 2;
                    var mod = stair % 2;
                    value = value * Convert.ToInt32(Math.Pow(2, pow)) + mod;
                    start = point + 2;
                }

                var stair2 = n - start;
                var pow2 = stair2 / 2;
                var mod2 = stair2 % 2;
                value = value + Convert.ToInt32(Math.Pow(2, pow2)) + mod2;
            }

            var ans = value % 1000000007;
            Console.WriteLine(ans);
        }
    }
}