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.*;
import java.util.function.Consumer;
import java.util.stream.Collectors;

public class Main {
    private static final Scanner scanner = new Scanner(System.in);
    private static final Consumer<List<String>> consumer = solve();

    public static void main(String[] args) {
        List<String> input = readInput();
        int N = Integer.valueOf(input.get(0).split(" ")[0]);
        memo = new long[N + 1];
        Arrays.fill(memo, 0);
        Set<Integer> dangerSet = input.stream().skip(1).map(Integer::valueOf).collect(Collectors.toSet());
        System.out.println(rec(N, dangerSet));
    }

    private static List<String> readInput() {
        final List<String> lineList = new ArrayList<>();
        while (scanner.hasNextLine()) {
            lineList.add(scanner.nextLine());
        }
        return lineList;
    }

    private static Consumer<List<String>> solve() {
        return args -> {
            int N = Integer.valueOf(args.get(0).split(" ")[0]);
            memo = new long[N + 1];
            Arrays.fill(memo, 0);
            Set<Integer> dangerSet = args.stream().skip(1).map(Integer::valueOf).collect(Collectors.toSet());
            System.out.println(rec(N, dangerSet));
        };
    }

    private static long[] memo;

    private static long rec(Integer n, Set<Integer> dangerSet) {
        if (n < 0 || dangerSet.contains(n)) {
            return 0;
        }
        if (n.equals(0)) {
            return 1;
        }
        if (memo[n] > 0) {
            return memo[n];
        }
        memo[n] = (rec(n - 1, dangerSet) + rec(n - 2, dangerSet)) % 1_000_000_007;
        return memo[n];
    }

}