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;
using System.Linq;
using System.Text;

namespace AtCoder
{
	public class Program
	{
		static void Main(string[] args)
		{
			const int x = 1000000007;

			int[] vs = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
			int N = vs[0];
			int M = vs[1];

			int[,] pt = new int[N + 3, 2];
			pt[0, 0] = 0;
			pt[0, 1] = 1;
			pt[1, 0] = 1;
			pt[1, 1] = 0;
			pt[2, 0] = 1;
			pt[2, 1] = 1;
			for (int i = 3; i <= N; i++) {
				pt[i, 0] = (pt[i - 1, 0] + pt[i - 1, 1]) % x;
				pt[i, 1] = pt[i - 1, 0];
			}

			int pos = 0, mv = 0;
			long ans = 1;
			for (int i = 0; i < M; i++) {
				int a = int.Parse(Console.ReadLine());
				if (a == pos) {
					Console.WriteLine(0);
					return;
				}
				mv = a - 1 - pos;
				ans = ans * (pt[mv, 0] + pt[mv, 1]) % x;
				pos = a + 1;
			}
			mv = N - pos;
			ans = ans * (pt[mv, 0] + pt[mv, 1]) % x;

			Console.WriteLine(ans);
		}
	}
}