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[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		TreeSet<Integer> set = new TreeSet<>();
		int sCount = 0;
		boolean first = true;
		for (int i = 0; i < k; i++) {
			set.add(arr[i]);
			if (i != k - 1 && arr[i] > arr[i + 1]) {
				first = false;
			}
		}
		if (first) {
			sCount++;
		}
		int count = 1;
		for (int i = k; i < n; i++) {
			if (set.first() == arr[i - k] && set.last() < arr[i]) {
				
			} else {
				boolean flag = true;
				for (int j = i - k + 1; j < i; j++) {
					if (arr[j] > arr[j + 1]) {
						flag = false;
						break;
					}
				}
				if (flag) {
					sCount++;
				}
				count++;
			}
			set.remove(arr[i - k]);
			set.add(arr[i]);
		}
		if (sCount > 1) {
			count = count - sCount + 1;
		}
		System.out.println(count);
	}
}