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 main() {
	long n,k,i,j,cur,ans,jud,res;
	cin >> n >> k;
	vector<long> a(n);
	set<long> b;
	for(i=0; i<n; i++){
		cin >> a[i];
	}
	for(i=0; i<k; i++){
		b.insert(a[i]);
	}
	auto itr=b.begin();
	ans=n-k+1;
	for(i=0; i<n-k; i++){
		itr=b.begin();
		jud=0;
		if(*itr==a[i]) jud++;

		b.erase(a[i]);
		b.insert(a[i+k]);
		itr=b.end();
		itr--;

		if(*itr==a[i+k]) jud++;

		if(jud==2){
			ans--;
		}
	}
	
	res=0; cur=0;
	for(i=1; i<n; i++){
		if(a[i-1]<a[i]){
			cur++;
			if(cur==k-1) res++;
		}else{
			cur=0;
		}
		
	}
	if(res>=2){
		ans-=res-1;
	}
	cout << ans;
	return 0;
}