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: Runtime Error)

import java.util.Scanner;
class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    int[] broken = new int[m];
    for(int i = 0; i < m; i++){
      broken[i] = Integer.parseInt(sc.next());
    }

    boolean possible = true;
    int succesive_safe = 1;
    int succesive_broken = 0;
    Long total_way = 1L;
    int[] fibonatti = {0,0,1};
    int next_broken = 0;

    for(int i = 0; i < n; i++){
      if(i + 1 != broken[next_broken]){
        if(succesive_safe == 0){
          succesive_broken = 0; 
        }
        succesive_safe++;
        
        fibonatti[0] = fibonatti[1];
        fibonatti[1] = fibonatti[2];
        fibonatti[2] = (fibonatti[1] + fibonatti[0]) % 1000000007;
        if(succesive_safe == 1){
          fibonatti[2] = 1;
        }
        System.out.println(fibonatti[2]);
        if(succesive_broken == 1){
          fibonatti[2] = 1;
        }
      }else if(succesive_broken == 0){
        succesive_broken++;
        total_way = total_way * fibonatti[2] % 1000000007;
        succesive_safe = 0;
        fibonatti[0] = 0;
        fibonatti[1] = 0;
        fibonatti[2] = 0;
        if(next_broken != m - 1){
          next_broken++;
        }
      }else{
        possible = false;
        break;
      }
    }
    total_way = total_way * fibonatti[2] % 1000000007;
    if(possible){
      System.out.println(total_way);
    }else{
      System.out.println(0);
    }
  }
}