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() {
	int n,k;
	cin>>n>>k;
	set<int> s;
	vector<int> v(n);
	int res=0;
	int c=1;
	bool f=false;
	for(int i=0,x;i<n;++i){
		scanf("%d",&x);
		v[i]=x;
		if(i && v[i]>v[i-1])
			++c;
		if(i && v[i]<v[i-1]){
			if(c>=k){
				--res;
				f=true;
			}
			c=1;
		}
		s.insert(x);
		if(i-k>=0)
			s.erase(v[i-k]);
		if(i>=k-1){
			bool ok=true;
			if(i-k>=0 && v[i]==*--s.end() && v[i-k]<*s.begin())
				ok=false;
			res+=ok;
		}
	}
	if(c>=k){
		--res;
		f=true;
	}
	if(f)
		++res;
	cout<<res<<endl;
	return 0;
}