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<iostream>
#include<vector>
#include<queue>
using namespace std;

int main(){
	int N,K,P[200000],sum=1,minD=0,maxD=0,ren=0,minus=0;
	bool exi[200001];
	priority_queue<int> top;
	priority_queue<int,vector<int>,greater<int>> bot;
	
	cin>>N>>K;
	
	for(int i=0;i<N;i++)cin>>P[i];

	for(int i=0;i<K;i++){
		top.push(P[i]);
		bot.push(P[i]);
	}
	for(int i=1;i<N;i++){
		if(P[i-1]>P[i])ren=0;
		else ren++;
		if(ren==K-1)minus++;
	}
	for(int i=K;i<N;i++){
		while(true){
			minD=bot.top();
			if(exi[minD])bot.pop();
			else break;
		}
		while(true){
			maxD=top.top();
			if(exi[maxD])top.pop();
			else break;
		}
		if(P[i-K]>minD||P[i]<maxD)sum++;
		exi[P[i-K]]=true;
		top.push(P[i]);
		bot.push(P[i]);
	}
	if(minus>=1)sum=sum-minus+1;
	cout<<sum<<endl;
	return 0;
}