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;
typedef long long ll;
typedef long long LL;
const long long M=1000000007;
#define ri register int 
#define rl register long long
int n,m,i,j,q[200005],l,r,a[200005],vis[200005],ans;
bool flag=false;
int main()
{
	l=1;
	r=0;
	scanf("%d %d",&n,&m);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
	for(i=1;i<=n;)
	{
		for(j=i;j<=n&&a[j]<a[j+1];j++);
		if(j-i+1>=m)
			if(flag)
				ans--;
			else
				flag=true;
		i=j+1;
	}
	for(i=1;i<m;i++)
	{
		while(l<=r&&a[q[r]]<a[i])
			r--;
		q[++r]=i;
	}
	for(i=m;i<=n;i++)
	{
		while(l<=r&&q[l]<=i-m)
			l++;
		while(l<=r&&a[q[r]]<a[i])
			r--;
		if(l>r)
			vis[i-m]++;
		q[++r]=i;
	}
	l=1;
	r=0;
	for(i=n;i>=n-m+2;i--)
	{
		while(l<=r&&a[q[r]]>a[i])
			r--;
		q[++r]=i;
	}
	for(i=n-m+1;i>=1;i--)
	{
		while(l<=r&&q[l]>=i+m)
			l++;
		while(l<=r&&a[q[r]]>a[i])
			r--;
		if(l>r)
			vis[i]++;
		q[++r]=i;
	}
	ans+=n-m+1;
	for(i=1;i<=n;i++)
		if(vis[i]==2)
			ans--;
	cout<<ans;
}