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 maxn=2e5+7;
typedef long long ll;
int a[maxn];
int main()
{
	int n,k;scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
	}
	int i=2;ll ans=n-k+1;ll now=0;ll res=0;
	for(int i=2;i<=n;i++)
	{
		int tmp=1;
		while(i<=n&&a[i]>a[i-1])
		{
			tmp++;i++;
		}
		if(tmp>=k)
		{
			res++;
		}
	}	
	set<int> se;
	for(int i=1;i<=k;i++) se.insert(a[i]);
	for(int i=k+1;i<=n;i++)
	{
		se.insert(a[i]);
		int mn=(*se.begin());int mx=(*se.rbegin());
		if(a[i]==mx && a[i-k]==mn)
		{
			ans--;
		}
		se.erase(a[i-k]);
	}
	if(!res)
	cout<<ans<<endl;
	else cout<<ans-res+1<<endl;
 }