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 main(){
	static int arr[200003]; int N , K;
	cin >> N >> K; for(int i = 1 ; i <= N ; ++i) cin >> arr[i];
	set < int > num; int ans = 1;
	for(int i = 1 ; i <= K ; ++i) num.insert(arr[i]);
	for(int i = K + 1 ; i <= N ; ++i){
		ans += *num.begin() != arr[i - K] || *--num.end() > arr[i];
		num.erase(arr[i - K]); num.insert(arr[i]);
	}
	bool flg = 0; int pre = -1 , cnt = 0;
	for(int i = 1 ; i <= N ; ++i){
		if(pre < arr[i]) ++cnt;
		else cnt = 1;
		pre = arr[i];
		if(cnt == K){flg = 1; --ans;}
	}
	cout << ans + flg; return 0;
}