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<cstdio>
#include<iostream>
#include<cstring>
#include<set>
using namespace std;
typedef long long ll;
const int N=2e5+10;
int a[N],n,k,cnt,c1,ans;
set<int> s;
int main(){
	cin>>n>>k;
	for (int i=1;i<=n;i++)scanf("%d",&a[i]);
	for (int i=1;i<=k;i++)s.insert(a[i]),cnt+=(i>1&&a[i]>a[i-1]);
	c1+=(cnt==k-1);ans=1;
	for (int i=k+1;i<=n;i++){
		if (a[i-k]<a[i-k+1])cnt--;
		if (a[i]>a[i-1])cnt++;
		if (a[i-k]!=*s.begin()||a[i]<*s.rbegin()){
			ans++;
			c1+=(cnt==k-1);
		}
		s.insert(a[i]);
		s.erase(a[i-k]);
	}
	if (c1)ans-=c1-1;
	cout<<ans<<endl;
}