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.Scanner;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.next());
    int m = Integer.parseInt(sc.next());
    int[] stair = new int[n+1];
    int mod = 1_000_000_007;
    for(int i=0;i<m;i++){
      stair[Integer.parseInt(sc.next())] = -1;
    }
    stair[0] = 1;
    for(int i=1;i<=n;i++){
      if(stair[i]==-1)continue;
      if(i>1){
        if(stair[i-2]!=-1)stair[i]+=stair[i-2];
        if(stair[i-1]!=-1)stair[i]+=stair[i-1];
        stair[i] = stair[i]%mod;
      }else{
        stair[i]+=1;
      }
    }
    System.out.print(stair[n]);
    System.out.flush();
  }
}