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.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();
		//故障している階段の段数を入れ込む配列宣言
		//初期値にfalseを入れておく。
		//壊れたところにtrue;
		boolean[] dest = new boolean[N];
		Arrays.fill(dest, false);
		for(int i = 0; i<M;i++) {
			int b = sc.nextInt();
			dest[b-1] = true;
		}
		long waru = 1000000007;
		//登れた階段の通りの値を確保する配列宣言
		//[0]は一段目と数える
		long[] anser = new long[N];

		if(N==1) {
			System.out.println(N);
		}else {
			//1,2段目の処理
			anser[0] = !dest[0]? 1:0;
			anser[1] = !dest[1]? anser[0]+1:0;
			//3段目からN段目までの処理
			for(int i = 2; i<N ; i++) {
				if(!dest[i]) {
					anser[i] = (anser[i-2] + anser[i-1]) % waru;
				}
			}
			System.out.println(anser[N-1]);
		}
	}
}