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;

int dp[200010];
int a[200010];

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n,k;
	cin>>n>>k;
	int ans=n-k+1;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	dp[1]=1;
	for(int i=2;i<=n;i++)
		if(a[i]>a[i-1])
			dp[i]=dp[i-1]+1;
		else
			dp[i]=1;
	for(int i=1;i<=n;i++)
		if(dp[i]>=k)
			ans--;
	for(int i=1;i<=n;i++)
		if(dp[i]>=k){
			ans++;
			break;
		}
	set<int> s;
	for(int i=2;i<=k;i++)
		s.insert(a[i]);
	for(int i=k+1;i<=n;i++){
		if(a[i-k]<*s.begin()&&*(--s.end())<a[i])
			if(dp[i]<k)
			ans--;
		s.erase(a[i-k+1]);
		s.insert(a[i]);
	}
	cout<<ans<<endl;
}