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;
	vector<int> P(N);
	for(auto &i:P)cin >> i;
	int ans=N-K+1;
	
	vector<bool> sorted(N+1,false);
	vector<int> check(N,0);
	for(int i=0;i<N-1;i++)sorted[i+1]=(P[i]<P[i+1]);
	
	int p=0;
	int c=0;
	while(p<=N){
		if(sorted[p])c++;
		else{
			if(c>=K-1)for(int i=0;i<c-K+2;i++)check[p-i-1]=1;
			c=0;
		}
		p++;
	}
	
	int S=accumulate(check.begin(),check.end(),0);
	if(S>1)ans-=S-1;
	else for(int i=0;i<N;i++)check[i]=0;
	
	set<int> s;
	for(int i=0;i<K;i++)s.insert(P[i]);
	for(int i=K;i<N;i++){
		auto l=s.begin();
		auto r=s.end();
		r--;
		if(*l==P[i-K] && *r<P[i] && check[i]==0)ans--;
		s.erase(P[i-K]);
		s.insert(P[i]);
	}
	cout << ans << endl;
	return 0;
}