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.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] a = new int[m];
        for (int i = 0 ; i < m ; i++) {
            a[i] = sc.nextInt();
        }
        int mod = 1000000007;
        long[] sum = new long[n + 1];
        sum[1] = 1;
        for (int i = 2 ; i < n + 1 ; i++) {
            sum[i] =   (long) sum[i - 1] + sum[i - 2];
            sum[i] %= mod;
        }
        for (int i = 0 ; i < m - 1 ; i++) {
            if (a[i + 1] - a[i] == 1) {
                System.out.println(0);
                return;
            }
        }
        long ans = 1l;
        int [] b = new int[m + 1];
        if (m == 1) {
            b[0] = a[0];
            b[1] = n - a[0];
        } else {
            b[0] = a[0];
            b[m] = n - a[m - 1];
            for (int i = 1 ; i < m ; i++) {
                if (a[i] - a[i - 1] == 0) {
                    b[i] = 1;
                } else {
                    b[i] = a[i] - a[i - 1] - 1;
                }
            }
        }
        for (int i = 0 ; i < m + 1 ; i++) {
            ans *= sum[b[i]] % mod;
        }
        System.out.println(ans % mod);
    }

}