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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.FileNotFoundException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {

		//    	File file = new File("src/in.txt");
		//    	Scanner sc = new Scanner(file);
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int M = sc.nextInt();
		int[] n = new int[N+1];

		for (int i = 1; i <= M; i++) {
			int x = sc.nextInt();
			n[x] = 1;
		}
		int cnt = 1;
		long ans = 1;
		for (int i=1;i<=N;i++) {
			if(n[i]!=1) {
				cnt++;
			} else {
				ans = mod(ans * mod(solve(cnt)));
				cnt =0;
			}
		}
		ans = mod(ans * mod(solve(cnt)));
		System.out.println(ans);
	}

	public static long solve(int N) {
		if (N==0) return 0;
		if (N==1||N==2)	return 1;
		long num1 = 1;
		long num2 = 1;
		long tmp = 1;
		for (int i = 1; i < N-1; i++) {
			tmp = mod(num1 + num2);
			num1 = mod(num2);
			num2 = mod(tmp);
		}
		return tmp;

	}

	public static long mod(long N) {

		return (long) N % 1000000007;

	}

}