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>
#include <iostream>
#include <set>
using namespace std;

int main() {
	//初期化
	int N;
	int K;
	cin >> N >> K;
	int array[N + 1];
	for (int i = 0; i < N; i ++){
		cin >> array[i];
	}	
	std::set<int> S;
	for (int i = 0; i < K; i ++){
		S.insert(array[i]);
	}

	//計算
	int ans;
	ans = 1;
	for (int i = K; i < N; i++){
		S.insert(array[i]);
		std::set<int>::iterator m = S.begin();
		std::set<int>::iterator M = S.end();
		M--;
		if (*M != array[i] || *m != array[i - K]){
			ans ++;
		}
		S.erase(array[i - K]);
	}
	int val = 0;
	int c = 1;
	for (int i = 0; i < N - 1; i++){
		if (array[i + 1] > array[i]){
			c++;
		}
		else{
			if (c >= K){
				val ++;
			}
			c = 1;
		}
	}
	if (c >= K){
		val ++;
	}
	if (val > 1){
		cout << ans - val + 1 << endl;
	}
	else{
		cout << ans << endl;
	}
}