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>
#define ll long long
using namespace std;
int a[200010],b[2000010],n,m;
int qzl[200010],qzr[200010],hzl[200010],hzr[200010]; 
int calc(int L,int R){
	return a[L]==min(hzl[L],qzl[R])&&
	a[R]==max(hzr[L],qzr[R]);
}
int main(){
	scanf("%d%d",&n,&m);
	int tag=-1;
	for(int i=0;i<n;i++){
		scanf("%d",&a[i]);
		if(i>0&&a[i]>a[i-1])b[i]=b[i-1]+1;
		else b[i]=1;
		if(b[i]>=m)tag++;
	}
	for(int i=0;i<n;i++){
		if(i%m==0)qzl[i]=qzr[i]=a[i];
		else qzl[i]=min(qzl[i-1],a[i]),qzr[i]=max(qzr[i-1],a[i]);
	}
	for(int i=n-1;i>=0;i--){
		if(i==n-1||(i+1)%m==0)hzl[i]=hzr[i]=a[i];
		else hzl[i]=min(hzl[i+1],a[i]),hzr[i]=max(hzr[i+1],a[i]);
	}
	int ans=n-m+1;
	for(int i=m-1;i<n-1;i++)
	if(b[i]<m&&b[i+1]<m&&calc(i-m+1,i+1))ans--;
	ans-=max(0,tag);cout<<ans;
	return 0;
}