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.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        long mod = 1000000000 + 7;
        int[] a = new int[M];
        boolean[] floors = new boolean[N + 1];
        Arrays.fill(floors, true);
        for (int i = 0; i < M; i++) {
            a[i] = sc.nextInt();
            floors[a[i]] = false;
        }

        Arrays.sort(a);
        int tmp = a[0];
        for (int i : a) {
            if ((i - tmp) == 1) {
                System.out.println(0);
                return;
            }
            tmp = i;
        }

        long ans = 1L;
        int now = 0;
        while (now < N - 1) {
            System.out.println(now);
            if (!floors[now + 1] && !floors[now + 2]) {
                System.out.println(0);
                return;
            }
            if (floors[now + 1] && floors[now + 2]) {
                ans = ((ans % mod) * 2) % mod;
                now += 2;
                continue;
            }
            now += floors[now + 1] ? 1 : 2;
        }

        System.out.println(ans);
    }
}