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.ArrayList;
import java.util.Scanner;
 
class Main {
	int n;
	int m;
	boolean[] a;
	long[] step;
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		Main m = new Main(sc);
		m.solve();
	}
	Main(Scanner sc){
		n = sc.nextInt();
		m = sc.nextInt();
		a = new boolean[n+1];
		step = new long[n+1];
		for(int i = 0; i <= n;i++){
			a[i] = true;
			step[i] = 0;
		}
		for(int i=0;i<m;i++){
			a[sc.nextInt()] = false;
		}
		step[0] = 1;
	}
	void solve(){
		for(int i = 0;i<n;i++){
			for(int j = i + 1;j <= Math.min(i+2, n);j++){
				if(a[j]){
					step[j] += step[i];
					step[j] %= 1000000007;
				}
			}
		}
		System.out.println(step[n]);
	}
}