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:
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 1000005
#define inf 1e9
#define eps 1e-10
using namespace std;

inline int read()
{
	int x=0,w=1; char c=getchar();
	while(c<'0'||c>'9') {if(c=='-') w=-1; c=getchar();}
	while(c<='9'&&c>='0') {x=(x<<1)+(x<<3)+c-'0'; c=getchar();}
	return w==1?x:-x;
}

int a[maxn],n,k,c,cnt,ans=1;
set <int> s;

int main()
{
	n=read(); k=read();
	for(int i=1;i<=n;i++) a[i]=read();
	for(int i=1;i<n;i++)
	{
		if(a[i]<a[i+1]) c++; else c=0;
		if(c==k-1) cnt++;
	}
	for(int i=1;i<=k;i++) s.insert(a[i]);
	for(int i=k+1;i<=n;i++)
	{
		s.erase(a[i-k]);
		if(a[i-k]>*s.begin()||a[i]<*s.rbegin()) ans++;
		s.insert(a[i]);
	}
	cout<<ans-max(0,cnt-1)<<endl;
	return 0;
}