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: Accepted)

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();

    Map<Integer, Long> memo = new HashMap<>();
    Set<Integer> broken = new HashSet<>();
    int[] a = new int[M];
    for (int i = 0; i < M; i++) {
      broken.add(sc.nextInt());
    }
    
    long ans = func(0, N, broken, memo);
    
    System.out.println(ans);
  }
  
  private static long func(int n, int N, Set<Integer> broken,
                          Map<Integer, Long> memo) {

    if (broken.contains(n) || N < n) {
      return 0;
    }
    if (n == N) {
      return 1;
    }
    Long cache = memo.get(n);
    if (cache != null) {
      return cache;
    }
    
    long value = func(n+1, N, broken, memo) % 1000000007
      + func(n+2, N, broken, memo) % 1000000007;
    memo.put(n, value % 1000000007);

    return value % 1000000007;
  }
}