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: Runtime Error)

import java.util.Scanner;

public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int m = scan.nextInt();

		long[] s = new long[100001];
		int len = s.length;
		long mod = 1000000007;

		s[0] = 1;
		s[1] = 1;

		int i;
		for(i = 2; i < len; i++)
			s[i] = (s[i - 1] + s[i - 2]) % mod;

		long[] a = new long[m];

		for(i = 0; i < m; i++) {
			a[i] = scan.nextInt();
			if(i != 0) {
				if(a[i] - a[i - 1] == 1) {
					System.out.println(0);
					return;
				}
			}
		}

		long start;
		long end;
		long ans = 1;
		for(i = 0; i < m; i++) {
			if(i == 0) {
				start = 0;
				end = a[i] - 1;
			}else {
				start = a[i - 1] + 1;
				end = a[i] - 1;
			}
			ans = (ans * s[(int)(end - start)]) % mod;
		}
		ans = (ans * s[(int)n - (int)(a[m - 1] + 1)]) % mod;
		System.out.println(ans);

	}
}