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>
#include <iostream>
#include <set>

using namespace std;

int main(){
	int n,k;
	cin>>n>>k;
	int a[n];
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	set<int> s;
	for(int i=0;i<k;i++){
		s.insert(a[i]);
	}
	int res=1,flag=1;
	int b[n],c=1;
	memset(b,0,sizeof(b));
	for(int i=1;i<n;i++){
		if(a[i]>a[i-1]) c++;
		else c=1;
		if(c>=k) b[i-k+1]=1;
	}
	if(b[0]) flag=0;
	for(int i=0;i<n-k;i++){
		if(a[i]!=*(s.begin()) || a[i+k]<*(s.rbegin())){
			if(b[i+1]){
				if(flag){
					res++;
					flag=0;
				}
			}
			else res++;
		}
		s.erase(a[i]);
		s.insert(a[i+k]);
	}
	cout<<res<<"\n";
	return 0;
}