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;

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

        int bi = M==0 ? -1: 0;
        ulong[] pattern = new ulong[N+1];
        pattern[0] = 1L;
        for (int i = 0; i < N; i++)
        {
            if (bi >= 0 && bi < M && A[bi] == i)
            {
                pattern[i] = 0L;
                bi++;
            }
            pattern[i+1] += pattern[i] % 1000000007UL;
            if(i+1<N) pattern[i+2] += pattern[i] % 1000000007UL;
        }

        Console.WriteLine(pattern[N] % 1000000007UL);
    }
}