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.Collections.Generic;

class ABC_129_C
{
    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        int M = int.Parse(input[1]);

        int[] A = new int[M+2];
        A[0] = 0;
        for (int i = 1; i < M+1; i++)
        {
            A[i] = int.Parse(Console.ReadLine());
            if(i>1 && A[i-1]+1==A[i])
            {
                Console.WriteLine(0);
                return;
            }
        }
        A[M+1] = N;

        long sum = 1;
        for (int i = 1; i < A.Length; i++)
        {
            int step = A[i] - A[i-1] - 1;
            if (M != 0)
            {
                if (i != 0 && i != M + 1) step -= 1;
            }
            else
            {
                step += 1;
            }
            if (step <= 0) continue;

            long pattern = 0;
            int up2 = 0;
            while(up2 * 2 <= step)
            {
                int n = step - up2;
                int k = up2;

                long c = Combination(n, k);
                pattern += c;
                up2++;
            }
            sum *= pattern;
        }

        Console.WriteLine(sum % 1000000007L);
    }

    static long Combination(int n, int k)
    {
        if (n == k || k == 0) return 1L;
        return Factorial(n, n-k+1) / Factorial(k, 1);
    }

    static long Factorial(int n, int k)
    {
        if(n==0) return 1L;
        if(n==k) return n;
        return n * Factorial(n-1, k);
    }
}