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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
class Program{
    static void Main(string[] args){
    var vals = Console.ReadLine().Split().Select(x => int.Parse(x)).ToList();
    int N=vals[0];
    int M=vals[1];
    //int a=0; //past
    //int A=0; //now
    List<int> A=new List<int>();
    A.Add(-1);
    for(int i=0;i<M;i++){
        A.Add(int.Parse(Console.ReadLine()));
    }
    A.Add(N+1);
    long ans=1;
    List<long> sum=new List<long>();
    List<long> list=new List<long>();
    list.Add(1);
    list.Add(1);
    for(int i=0;i<N+1;i++){
        list.Add(list[i]+list[i+1]);
    }

    for(int i=0;i<M+1;i++){
        //A = int.Parse(Console.ReadLine());
        var diff=A[i+1]-A[i]-2;
        if(A[i+1]!=1&&diff<0){
            ans=0;
            break;
        }
       /* var tmp=(diff/3)*3;
        if(diff==0){
            tmp=1;
        }
        else if(diff%3==2){
        tmp=tmp*2;
        }*/
        sum.Add(list[diff]);

    }
    foreach(long s in sum){
        ans=ans*s%1000000007;
    }
    Console.WriteLine(ans);
    }
}