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 n, k, x[200005], ans = 1, cnt;
bool g;
set<int> s;

int main() {
	scanf("%d%d", &n, &k);
	for (int i = 0; i < n; i++) {
		scanf("%d", x + i);
		if (i && x[i] > x[i - 1])
			cnt++;
		if (i - k >= 0 && x[i - k + 1] > x[i - k])
			cnt--;
		// printf("cnt=%d k-1=%d %d\n", cnt, k - 1, x[i]);
		s.insert(x[i]);
		if (i >= k) {
			if (x[i] != *s.rbegin() || x[i - k] != *s.begin()) {
				if (cnt != k - 1 || !g) {
					ans++;
					// printf("%d\n", x[i]);
				}
			}
			s.erase(x[i - k]);
		}
		if (cnt == k - 1)
			g = 1;
	}
	printf("%d\n", ans);
}