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 AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] NM = Console.ReadLine().Split(' ');
            int N = int.Parse(NM[0]);
            int M = int.Parse(NM[1]);
            int[] step_list = new int[N];
            int[] obstacles = new int[M];
            for(int i = 0; i < M; i++)
            {
                int ind = int.Parse(Console.ReadLine());
                step_list[ind] = 1;
                obstacles[i] = ind;
            }
            for (int i = 0; i < N-1; i++)
            {
                // Check for 2x damaged step first
                if (step_list[i] == 1 && step_list[i+1] == 1)
                {
                    // Game over. set 0
                    Console.WriteLine("0");
                    return;
                }
            }
            long cases = 1;
            for (int i = 0; i < M; i++)
            {
                int diff = 0;
                // Calc step count diff between obstacles
                switch (i)
                {
                    case 0:
                        diff = obstacles[i];
                        break;
                    default:
                        diff = obstacles[i] - obstacles[i - 1];
                        break;
                }
                // Calc step types (fibonacci)
                long[] fib_array = new long[] { 0, 1 };
                long fib = 1;
                for (int j = 0; j < diff - 1; j++)
                {
                    fib = fib_array[0] + fib_array[1];
                    fib_array[0] = fib_array[1];
                    fib_array[1] = fib;
                }
                cases *= fib % 1000000007;
            }
            // last 1 pos
            int diff_last = N - obstacles[M - 1];
            // Calc step types (fibonacci)
            long[] fib_array_last = new long[] { 0, 1 };
            long fib_last = 1;
            for (int j = 0; j < diff_last - 1; j++)
            {
                fib_last = fib_array_last[0] + fib_array_last[1];
                fib_array_last[0] = fib_array_last[1];
                fib_array_last[1] = fib_last;
            }
            cases *= fib_last % 1000000007;


            Console.WriteLine((cases%1000000007).ToString());
        }
    }
}