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 {

	public static final long MOD = 1000000007L;

	public static void main(String args[]) {

		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();

		long[] a = new long[M];
		long[] steps = new long[N+1];
		for(int i=0;i<N;i++) {
			steps[i] = 0;
		}

		for(int i=0;i<M;i++) {
			a[i] = sc.nextLong();
			steps[(int) a[i]] = -1;
		}

		steps[0] = 1;
		steps[1] = (steps[1] == -1) ? -1 : 1;
		for(int i=2;i<N+1;i++) {

			if(steps[i] == -1) continue;

			if(steps[i-1] == -1 && steps[i-2] == -1) {
				System.out.println(0);
				return;
			}

			if(steps[i-1] == -1) {
				steps[i] = steps[i-2];
			}else if(steps[i-2] == -1) {
				steps[i] = steps[i-1];
			}else {
				steps[i] = (steps[i-1] + steps[i-2])%MOD;
			}
		}
		System.out.println(steps[N]%MOD);
	}
}