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;
const int SIZE=200000+50;
int a[SIZE],q[SIZE];
int vis[SIZE];
int minn[SIZE],maxx[SIZE];

int main()
{
    int n,k;
	scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++)  scanf("%d",&a[i]);
    int len=1;
    int same=0;
    for(int i=2;i<=n;i++)
    {
    	if(a[i]>a[i-1]) len++;
    	else
    	{
    		len=1;
		}
		if(len==k) same++;
	}
    int l=1,r=0;
    for(int i=1;i<=n;i++){
        while(r>=l && a[q[r]]>=a[i])r--;
        q[++r]=i;
        while(r>=l && q[l]<i-(k-1)+1)l++;
        minn[i]=a[q[l]];
    }
    l=1,r=0;
    for(int i=1;i<=n;i++){
        while(r>=l && a[q[r]]<=a[i])r--;
        q[++r]=i;
        while(r>=l && q[l]<i-(k-1)+1)l++;
        maxx[i]=a[q[l]];
    }
    int cnt=0;
    for(int i=k;i<=n-1;i++){
    	if(a[i-k+1]<=minn[i]&&a[i+1]>=maxx[i])
    	{
    		cnt++;
		}
	}
	//if(same>=2) same=1;
	printf("%d\n",n-k+1-cnt-max(same-1,0));
}