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.*;
 
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
 
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] a = new int[M + 1];
        if(M==0){
            a[0] = 0;
        }
        else{
            a[0] = sc.nextInt();
        }

        for(int i=1; i<M; i++){
            a[i] = sc.nextInt();
            if(a[i]==a[i-1]+1){
                System.out.println(0);
                return;
            }
        }

        int[] ans = new int[N + 1];
        ans[0] = 1;
        int x = 0;
        if(a[0]==1){
            ans[1] = 0;
            x += 1;
        }
        else{
            ans[1] = 1;
        }
        for(int i=2; i<=N; i++){
            if(i==a[x]){
                ans[i] = 0;
                x += 1;
            }
            else{
                ans[i] = (ans[i - 1] + ans[i - 2]) % 1000000007;
            }
        }
        System.out.println(ans[N]);
    }
}