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: Wrong Answer)

import java.util.*;
import java.lang.*;

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+2];

            for(int i = 1 ; i <= M ; i++){
                A[i] = sc.nextInt();
            }
            A[0] = -1;
            A[M+1] = N+1;
            sc.close();

            /*
            for(int i = 0 ; i <=M+1 ; i++){
                System.out.println(A[i]);
            }
            */
            long[] dp = new long[N+1];
            dp[0] = 1;
            dp[1] = 1;

            long ans = 1;
            long INF = 1000000007;
            boolean flag = true;
            for(int i = 1 ; i <= M+1 ; i++){
                int tmp = (A[i]-1) -(A[i-1]+1);
                if(tmp<0){
                    flag = false;
                    break;
                }
                if(dp[tmp] != 0){
                    ans *= dp[tmp];
                }
                else{
                    for(int j = 2 ; j <= tmp ; j++){
                        dp[j] =dp[j-2] + dp[j-1];
                    }
                    ans *= dp[tmp];
                }
            }
            if(!flag){
                System.out.println("0");
            }
            else{
                System.out.println(ans%INF);
            }
    }

}