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;

public class Test
{
	public static void Main()
	{
		// your code goes here
		
		var b = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
		int n = b[0];
		int m = b[1];
		
		int[] a = new int[m];
		for(int c=0; c!=m; c++){
			a[c] = int.Parse(Console.ReadLine());
		}
		
		int[] sa =new int[m+1];
		double[] f = new double[m+1];
		int[] g = new int[m+1];
		
		sa[0] = a[0]-1;
		if(sa[0]!=0){
			f[0] = Math.Round(((Math.Pow(((1+(Math.Sqrt(5)))/2),(sa[0]+1)))-(Math.Pow(((1-(Math.Sqrt(5)))/2),(sa[0]+1))))/(Math.Sqrt(5)));
			g[0] = Convert.ToInt32(f[0]);
		}else{f[0]=0;g[0]=0;}
		int last = g[0];
		
		for(int d=1; d!=m; d++){
			sa[d] = a[d] - a[d-1] -1;
			if(sa[d]!=0){
				f[d] = Math.Round(((Math.Pow(((1+(Math.Sqrt(5)))/2),(sa[d]+1)))-(Math.Pow(((1-(Math.Sqrt(5)))/2),(sa[d]+1))))/(Math.Sqrt(5)));
				g[d] = Convert.ToInt32(f[d]);
			}else{f[d]=0;g[d]=0;}
			last = last*g[d];
		}
		
		sa[m] = n - a[m-1] -1;
		if(sa[m]!=0){
			f[m] = Math.Round(((Math.Pow(((1+(Math.Sqrt(5)))/2),(sa[m]+1)))-(Math.Pow(((1-(Math.Sqrt(5)))/2),(sa[m]+1))))/(Math.Sqrt(5)));
			g[m] = Convert.ToInt32(f[m]);
		}else{f[m]=0;g[m]=0;}
		last = last*g[m];
		
		last = last%1000000007;
		Console.WriteLine(last);
		
	}
}