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+5; 
int n,k;
int a[maxn];
set<int>s;
int ans=1;
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;i++) cin>>a[i];
	for(int i=1;i<=k;i++) s.insert(a[i]);
	for(int i=k+1;i<=n;i++){
		ans+=*s.begin()!=a[i-k]||*--s.end()>a[i];
		s.erase(a[i-k]); s.insert(a[i]);
	}
	bool flag=0;
	int cnt=0;
	a[0]=-1;
	for(int i=1;i<=n;i++){
		if(a[i-1]<a[i]) cnt++;
		else cnt=1;
		if(cnt==k){
			flag=1;
			ans--;
		}
	}
	printf("%d\n",ans+flag);
	return 0;
}