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;

namespace C_ABC129
{
    class MainClass
    {

        static int[] s;
        static long[] dp;
        static long MOD;

        public static void Main(string[] args)
        {
            s = Array.ConvertAll(Console.ReadLine().Split().ToArray(), int.Parse);
            dp = new long[s[0] + 1];
            for (int i = 0; i <= s[0]; i++)
            {
                dp[i] = -1;
            }
            var alst = new List<int>();
            for (int i = 0; i < s[1]; i++)
            {
                int a = int.Parse(Console.ReadLine());
                alst.Add(a);
                dp[a] = 0;
            }

            MOD = 1000000007;

            dp[0] = 1;
            if (dp[1] != 0)
            {
                dp[1] = 1;
            }

            Console.WriteLine(Dp(s[0]));

        }

        public static long Dp(int n)
        {

            if (dp[n] != -1)
            {
                // Console.Write("DP: {0} ", n);
                //   Console.WriteLine("ans: {0} ", dp[n]);
                return dp[n];
            }
            else
            {
                long ans = Dp(n - 1) + Dp(n - 2);
                dp[n] = ans % MOD;
                //           Console.Write("DP: {0} ", n);
                // Console.WriteLine("ans: {0} ", dp[n]);
                return dp[n];
            }
        }
    }
}