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 P[200005];

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

	set<int> S;
	int cnt = 0;
	for (int i = 0; i < K; ++i) {
		S.insert(P[i]);
		if (i) cnt += P[i - 1] < P[i];
	}
	
	int ans = 0;
	bool inorder = cnt == K - 1;
	bool t = cnt != K - 1;
	for (int i = 0; i < N - K; ++i) {
		bool b = P[i] == *S.begin();
		S.erase(P[i]);
		cnt -= P[i] < P[i + 1];
		S.insert(P[i + K]);
		cnt += P[i + K - 1] < P[i + K];
		if (cnt == K - 1) inorder = true;
		b &= P[i + K] == *S.rbegin();
		if (!b && cnt != K - 1) ++ans;
	}

	cout << ans + inorder + t << '\n';
}