Problem: Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

* Choose K consecutive elements in P and sort them in ascending order.



Find the number of permutations that can be produced as P after the operation.

Constraints

* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
P_0 P_1 \cdots P_{N-1}


Output

Print the number of permutations that can be produced as P after the operation.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

10 4
2 0 1 3 7 5 4 6 8 9


Output

6

Solution (in JAVA):

Solution:
import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int k = sc.nextInt();
    int[] p = new int[n];
    for(int i=0;i<n;i++)p[i]=sc.nextInt();
    int ans = 1;
    TreeSet<Integer> ts = new TreeSet<>();
    for(int i=0;i<n;i++){
      ts.add(p[i]);
      if(i>=k){
        if(ts.first()!=p[i-k]||ts.last()!=p[i])ans++;
        ts.remove(p[i-k]);
      }
    }
    int not = 0;
    int cnt = 1;
    for(int i=1;i<n;i++){
      if(p[i-1]<p[i]){
        cnt++;
        if(cnt==k){
          not++;
        }
      }else cnt=1;
    }
    if(not>=2)System.out.println(ans-(not-1));
    else System.out.println(ans);
  }
}