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.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        int a[] = new int[m + 2];
        for (int i = 1; i <= m; i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        sc.close();
        a[0] = -1;
        a[m + 1] = n + 1;
        List<Integer> b = new ArrayList<>();
        for (int i = 1; i <= m + 1; i++) {
            if (a[i] - a[i - 1] == 1) {
                System.out.println(0);
                return;
            }
            b.add(a[i] - a[i - 1] - 1);
        }
        long memo[] = new long[n + 2];
        memo[1] = 1;
        memo[2] = 1;
        for (int i = 3; i <= n + 1; i++) {
            memo[i] = memo[i - 1] + memo[i - 2];
            memo[i] %= 1_000_000_007;
        }
        long ans = 1;
        for (int i = 0; i < b.size(); i++) {
            ans *= memo[b.get(i)];
            ans %= 1_000_000_007;
        }
        System.out.print(ans);
    }
}