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;
const int N = 200005;
int n, k, p[N], ps[N], good[N], lnk[N];
set<int> st;
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n >> k;
	for (int i = 0; i < n; i++) cin >> p[i];
	ps[0] = 0;
	for (int i = 1; i < n; i++) ps[i] = ps[i - 1] + (p[i] > p[i - 1] ? 1 : 0);
	int ans = 0;
	for (int i = 0; i < n - k + 1; i++) {
		if (ps[i + k - 1] - ps[i] == k - 1) good[i] = 1, ans = 1;
		else good[i] = 0;
	}
	for (int i = 0; i < k - 1; i++) st.insert(p[i]);
	for (int i = 0; i < n - k; i++) {
		st.erase(p[i]);
		st.insert(p[i + k - 1]);
		if (!good[i] && !good[i + 1] && *st.begin() > p[i] && *st.rbegin() < p[i + k]) lnk[i] = 1;
	}
	for (int i = 0; i < n - k + 1; i++) if (!good[i]) {
		int j = i;
		while (j < n - k && !good[j + 1] && lnk[j]) j++;
		ans++;
		i = j;
	}
	cout << ans << endl;
	return 0;
}