Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
typedef long long ll;
#define  rep(i,a,b)for(long long i=a;i<b;++i)
#define  rrep(i,a,b)for(int i=a;i>=b;--i)
#define  yesno(flag)if(flag)cout<<"Yes"<<endl; else cout<<"No"<<endl;
using namespace std;
const ll INF=1000000000000LL;
const ll r197=1000000007;
typedef pair<int,int>P;
typedef pair<int,P>Pa;
bool Inframe(int a,int b,int c,int d,int h,int w){
	if(a+b>=0&&a+b<h&&c+d>=0&&c+d<w)return true;
	return false;
}

int n,k,p[200005],ans=1;
string str;
priority_queue<long long ,vector<long long> > que;
set<int> st;
bool a=0;
int main() {
	cin>>n>>k;
	rep(i,0,n)cin>>p[i];
	rep(i,0,k){
		st.insert(p[i]);
	}
	int c=1;
	bool f=0;
	rep(i,1,n){
		if(p[i-1]>p[i]){
			if(c>=k){
				--ans;
				f=true;
			}
			c=0;
		}
		c++;
	}
	if(c>=k){
		--ans;
		f=true;
	}
	if(f)ans++;

	for(int i=1;i<n-k+1;++i){
		auto itr1=st.begin();
		int it=*itr1;
		st.erase(p[i-1]);
		st.insert(p[i+k-1]);
		auto itr2=st.end();
		itr2--;
		if(it==p[i-1]&&*itr2==p[i+k-1])--ans;
		++ans;
	}
	cout<<ans<<endl;
	return 0;
}