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();

        List<Integer> holeList  = new ArrayList<>();

        for (int i = 0; i < m; i++){
            holeList.add(sc.nextInt());
        }

        long count = 0;
        long countOneBefore = 1;
        long countTwoBefore = 0;

        int holeIndex = 0;
        int holeStair = 0;
        if (holeList.size() != 0){
            holeStair = holeList.get(holeIndex);
        }

        for (int i = 0 ; i < n; i++){

            if (holeStair == (i + 1)){
                // 穴が開いている場合
                count = 0;
                countTwoBefore = countOneBefore;
                countOneBefore = count;

                holeIndex += 1;
                holeStair = holeList.get(Math.min(holeIndex, m - 1));
            }else {
                count = countOneBefore + countTwoBefore;
                if (count >= 1000000007L){
                    count = count % 1000000007L;
                }
                countTwoBefore = countOneBefore;
                countOneBefore = count;
            }
        }

        System.out.println(count);
    }

}