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;

#define Debug(x) x
typedef int regular_int;
// #define int ll
typedef long long ll;

int P[300000];


regular_int main() {
	ios_base::sync_with_stdio(false);
	cout << setprecision(12) << fixed;

	int N, K;
	cin >> N >> K;
	for(int i = 0; i < N; ++i) {
		cin >> P[i];
	}
	int pos =  - 1;
	set<int > val;
	for(int i = 0; i < K; ++i) {
		val.insert(P[i]);
		if(i > 0 && P[i] < P[i - 1]) {
			pos = i;
		}
	}
	bool sum = pos < 0;
	int res = pos >= 0;
	bool active = *val.begin() != P[0];

	for(int i = K; i < N; ++i) {
		val.erase(P[i - K]);
		val.insert(P[i]);

		if(P[i] < P[i - 1]) {
			pos = i;
		}

		if(pos <= i - K + 1) {
			sum = true;
			active = false;
		} else {
			if(active || *(--val.end()) != P[i]) {
     //           cout << "i: " << i << endl;
				++res;
			}

		}
		active = *val.begin() != P[i - K + 1];

	}
	cout << res + sum << endl;
	return 0;
}