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 <iostream>
#include <vector>
#include <set>
using namespace std;
typedef long long int ll;

int main(){
	int n,k; cin >> n >> k;
	vector<int> a(n);
	for(int i=0;i<n;i++){
		cin >> a[i];
	}
	int sorted=0;
	int cnt=0;
	for(int i=0;i<n-1;i++){
		if(a[i]<a[i+1]){
			cnt++;
		}
		else cnt=0;
		if(cnt==k-1)sorted++;
	}
	set<int> s;
	for(int i=0;i<k;i++){
		s.insert(a[i]);
	}
	int ans=1;
	for(int i=0;i<n-k;i++){
		ans++;
		auto it=s.begin();
		auto itt=s.end(); itt--;
		if(a[i]==*it&&a[i+k]>*itt)ans--;
		s.erase(a[i]);
		s.insert(a[i+k]);
	}
	if(sorted)ans-=sorted-1;
	cout << ans << endl;
}