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.Scanner;
import java.util.Set;
import java.util.TreeSet;

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;

        Set<Integer> set = new TreeSet<>();
        for (int i=0; i<n; i++){
            set.add(p[i]);
            if (i>=k){
                if (((TreeSet<Integer>) set).first()!=p[i-k] || ((TreeSet<Integer>) set).last()!=p[i]){
                    ans++;
                }
                set.remove(p[i-k]);
            }
        }

        int notChange = 0;

        int cnt = 1;

        for (int i=0; i<n-1; i++){
            if (p[i]<p[i+1]){
                cnt++;
                if (cnt==k){
                    notChange++;
                }
            }else {
                cnt = 1;
            }
        }

        if (notChange>=2){
            notChange -= 1;
        }else {
            notChange = 0;
        }
        System.out.println(ans-notChange);

    }
}