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: Time Limit Exceeded)

import java.util.*;

public class Main {

  public static int N;
  public static int M;
  public static int[] a;
  public static long mod = 1000000007;
  public static int count;

  public static void main (String[] args) {

    Scanner sc = new Scanner(System.in);
    
    N = sc.nextInt();
    M = sc.nextInt();
    a = new int[M];
    
    for (int i = 0; i < M; i++) {
      a[i] = sc.nextInt();
    }

    sc.close();

    dfs(0,0);

    System.out.println(count % mod);
    
  }

  public static void dfs(int i, int j){

    if (N <= i) {
      count++;
      //System.out.println("OK");
      return;
    }
    
    //System.out.print(i + " ");

    if (j < a.length) {

      if (a[j] < i) {    

        if (j + 1 < a.length) {
          j++;
        }

        //System.out.println("jを"+j+"（"+a[j]+"）に変えます");
      }

      if (i == a[j]){
        //System.out.println(i+"の穴に落ちます");
        return;  
      }

    }

    dfs(i+1,j);
 
    if (i != N - 1) {
      dfs(i+2,j);
    }

  }

}