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>
#define Int int64_t

using namespace std;

int main() {
	int N, K;
	cin >> N >> K;
	vector<int> a(N);
	for (int i = 0; i < N; ++i) { cin >> a[i]; }

	set<int> st1, st2;
	for (int i = 0; i < K; ++i) {
		st1.insert(a[i]);
		st2.insert(a[i]);
	}

	int ans = 1;
	for (int i = 1; i + K <= N; ++i) {
		int min_a = *st1.lower_bound(-1);
		st2.insert(a[i+K-1]);
		auto max_itr = st2.upper_bound(a[i+K-1]);
		if (min_a != a[i-1] || (max_itr != st2.end())) {
			++ans;
		}
		st1.erase(a[i-1]);
		st1.insert(a[i+K-1]);
		st2.erase(a[i]);
	}

	int cnt = 1;
	int x = 0;
	for (int i = 1; i < a.size(); ++i) {
		if (a[i - 1] < a[i]) {
			++cnt;
		} else {
			if (cnt >= K) { ++x; }
			cnt = 1;
		}
	}
	if (cnt >= K) { ++x; }
	ans -= (x > 1 ? x - 1 : 0);
	cout << ans << endl;

	return 0;
}