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();

        List<Integer> list = new ArrayList<Integer>();
        for(int tmp = 0; tmp<m; tmp++){
            int w = sc.nextInt();

            list.add(w);
        }
        list.add(n);
        List<Long> rootlist = new ArrayList<Long>();
        rootlist.add(0l);
        rootlist.add(1l);
        rootlist.add(2l);
        for(int tmp = 3; tmp <= n; tmp++){
            rootlist.add(rootlist.get(tmp - 1) + rootlist.get(tmp -2));
        }

        long result = 1;

        if(list.size() == 0){
            result = rootlist.get(n);
        }else{

            if(list.get(0) != 1){
                result *= rootlist.get(list.get(0) - 1);
            }

            for(int tmp = 1; tmp < list.size(); tmp++){
                result %= 1000000000;
                long kakeru = 1;
                if(n != list.get(tmp) + 1) {
                    kakeru = rootlist.get((list.get(tmp) - list.get(tmp - 1)) - 1);
                }
                kakeru %= 1000000000;
                result *= kakeru;

            }
        }


        long newresult = 0;
        if(result != 0) {
            newresult = result % 1000000007;
        }
        System.out.println(newresult);
    }
}