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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
    public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);

      int n=sc.nextInt();
      int m=sc.nextInt();

      int ans = 1;
      int flag = 1;

      int[] a = new int[m];

      for(int i=0;i<m;i++){
        a[i]=sc.nextInt()-1;
      }

      //////////ERROR//////////////////////
      for(int i=0;i<m-1;i++){
        if(a[i+1]==a[i]+1){
          flag = 0;
          break;
        }
      }
      ////////////////////////////////////

      //////////broken check///////////////
      int[] stair = new int[n];
      for(int i=0;i<n;i++){
        stair[i] = i;
        for(int j=0;j<m;j++){
          if(i==a[j]){
            stair[i] = -1;
          }
        }
      }
      /////////////////////////////////////

      ///////////////////////////////////////////////
      for(int i=-1;i<n-2;i++){
        if(stair[i+1]!=-1 && stair[i+2]!=-1){
          ans *= 2;
          ans = ans % 1000000007;
          i++;
        }
        else if(stair[i+1]!=-1){
          i+=2;
        }
        else{
          i++;
        }
      }
      ///////////////////////////////////////////////




      if(flag==0){
        System.out.println("0");
      }
      else{
        System.out.println(ans);
      }
/*
      for(int i=0;i<n;i++){
        System.out.print("stair=");
        System.out.println(stair[i]);
      }
*/

    }
}