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;
namespace I_am_the_brown_coder{
    class Inonoa{
        static void Main(){
            string[] n_m = Console.ReadLine().Split();
            int n = int.Parse(n_m[0]);
            int m = int.Parse(n_m[1]);

            bool[] broken = new bool[n];
            for(int i=0;i<m;i++){
                broken[int.Parse(Console.ReadLine())-1] = true;
            }

            if(n==1){
                Console.WriteLine(1);
                return;
            }

            long[] dp = new long[n];
            if(broken[0]){
                dp[0] = 0;
            }else{
                dp[0] = 1;
            }
            
            if(broken[1]){
                dp[1] = 0;
            }else{
                if(broken[0]){ //1段目が壊れてたら飛ばすしかない
                    dp[1] = 1;
                }else{
                    dp[1] = 2;
                }
            }

            for(int i=2;i<n;i++){
                if(broken[i]){
                    dp[i] = 0;
                }else{
                    dp[i] = (dp[i-2] + dp[i-1])%1000000007;
                }
            }

            Console.WriteLine(dp[n-1]);

        }
    }
}