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.

Examples

Input

6 1
3


Output

4


Input

10 2
4
5


Output

0


Input

100 5
1
23
45
67
89


Output

608200469
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];
        int b[]=new int[m+1];
        int fib[]=new int[n+2];
        fib[0]=0;
        fib[1]=1;
        for(int i=2;i<n+2;i++){
            fib[i]=fib[i-1]+fib[i-2];
            fib[i]%=1000000007;
        }
        int po=-1;
        for(int i=0;i<m;i++){
            a[i]=sc.nextInt();
            b[i]=a[i]-po-1;
            po=a[i];
        }
        b[m]=n-po;
        long ans=1;
        for(int i=0;i<m+1;i++){
            //System.out.println(b[i]);
            ans*=fib[b[i]];
            ans%=1000000007;
        }
        System.out.println(ans);
    }
}
