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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int num[200010], n, k; set<int> s;
int main() {
	scanf("%d%d", &n, &k);
	for (int i = 1; i <= n; i++) scanf("%d", &num[i]);
	int res = 1, ct = 0, hh = 0;
	for (int i = 1; i <= k; i++) s.insert(num[i]);
	for (int i = 1; i < n; i++) {
		if (num[i] < num[i + 1]) ct++;
		else ct = 0;
		if (ct == k - 1) hh++;
	}
	for (int i = k + 1; i <= n; i++) {
		s.erase(num[i - k]);
		if (num[i - k] > *s.begin() || num[i] < *s.rbegin()) 
			res++;
		s.insert(num[i]);
	}
	printf("%d\n", res - max(0, hh - 1));
}