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.Scanner;

public class Main {
	static long mod = 1_000_000_007;
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		boolean[] step = new boolean[in.nextInt()];
		int bs = in.nextInt();
		int[] bsnum = new int[bs];
		for (int i = 0; i < bs; i++) {
			bsnum[i] = in.nextInt();
		}
		in.close();
		for (int i = 0; i < step.length; i++) {
			step[i] = true;
		}
		for (int b : bsnum) {
			step[b - 1] = false;
			if (b != 1 && !step[b - 2]) {
				System.out.println(0);
				return;
			}
		}
		long[] dp = new long[step.length + 1];
		dp[0] = 1L;
		for (int i = 0; i < dp.length - 1; i++) {
			if (!step[i]) {
				dp[i + 1] = 0;
				continue;
			}
			if (i == 0) {
				dp[i + 1] = 1L;
            	continue;
			}
			dp[i + 1] = dp[i] + dp[i - 1];
			dp[i + 1] %= mod;
		}
		System.out.println(dp[step.length]);
	}
}