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>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
typedef long long ll;

ll n,k,p[200000],x[200000];
set<int> st;

int main(){
    cin>>n>>k;
    ll ans=n-k+1;
    rep(i,n)cin>>p[i];
    rep(i,k)st.insert(p[i]);
    rep(i,n-k){
        st.insert(p[i+k]);
        auto itr=st.end();
        itr--;
        if(*st.begin()==p[i]&&*itr==p[i+k])ans--;
        st.erase(p[i]);
    }
    int aaa=0;
    for(int i=1;i<n;i++){
        if(p[i-1]<p[i])x[i]=x[i-1]+1;
        if(x[i]==k-1)ans--,aaa=1;
    }
    cout<<ans+aaa<<endl;
}