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 final int MOD = 1000000007;

	public static void main(String[] args) {
	
		Scanner sc = new Scanner(System.in);
		
		int N = sc.nextInt();
		int M = sc.nextInt();
		boolean[] hole = new boolean[N+1];
		for(int i=0; i<N+1; i++) {
			hole[i] = true;
		}
		
		int[] a = new int[M];
		
		for(int i=0; i<M; i++) {
			a[i] = sc.nextInt();
			hole[a[i]] = false;
		}
		
		int[] dp = new int[N+1];
		dp[0] = 1;
		if(hole[1]) {dp[1]=1;}
		for(int i=2; i<=N; i++) {
			if(hole[i-1]) {dp[i] = (dp[i] + dp[i-1])%MOD ;}
			if(hole[i-2]) {dp[i] = (dp[i] + dp[i-2])%MOD ;}
		}
		
		System.out.println(dp[N]);
	}
}