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: Wrong Answer)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author champon
 */

//<editor-fold desc="definitions">
#include <bits/stdc++.h>
#define se cout << "test ok" << endl;
#define sp << " " <<
#define enl "\n"
using namespace std;
using ll=long long;
using ld=long double;
using vi = vector<int>;
using vii = vector<vector<int>>;
using viii = vector<vector<vector<int>>>;
using vl = vector<ll>;
using vll = vector<vector<ll>>;
using vlll = vector<vector<vector<ll>>>;
using vc = vector<char>;
using vcc = vector<vector<char>>;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
ll mod = ll(1e9)+7;
ll inf = ll(1e18);
void bl(bool b, ostream& out=cout){ out << (b ? "Yes" : "No") << endl; }
void bl2(bool b, ostream& out=cout){ out << (b ? "YES" : "NO") << endl; }
template<typename T> inline bool chmax(T &a, T b){ if(a<b){a=b; return true;} return false; }
template<typename T> inline bool chmin(T &a, T b){ if(a>b){a=b; return true;} return false; }
int dx[] = {1, 0, -1, 0, 1, -1, 1, -1};
int dy[] = {0, 1, 0, -1, 1, -1, -1, 1};

#ifndef INCLUDE_DEBUG_HPP
#define INCLUDE_DEBUG_HPP

#define TO_STRING(varName) # varName
#include <iostream>
#include <vector>
#include <map>
using namespace std;

namespace dbg {
    using ll = long long;

    class Debug {
        void prefix() { cout << "\033[7m\033[35m" << " DEBUG " << "\033[0m" << endl; }

        void out_helper(){ cout << endl; }

        void out_with_name_helper(){ cout << endl; }

        template<typename T1, typename... T2>
        void out_helper(T1 v, T2... args);

        template<typename T1, typename... T2>
        void out_with_name_helper(string s, T1 v, T2... args);

        // value
        template<typename T>
        void print(T val);

        // pair
        template<typename A, typename B>
        void print(pair<A, B> p);

        // tuple
        template<typename A, typename B, typename C>
        void print(tuple<A, B, C> t);

        // vector
        template<typename T>
        void print(vector<T> &vec);

        // set
        template<typename T>
        void print(set<T> &st);

        // map
        template<typename A, typename B>
        void print(map<A, B> mp);
    public:
        Debug(){}

        template<typename... T>
        void out(T... args){
            prefix();
            out_helper(args...);
        }

        template<typename... T>
        void out_with_name(T... args){
            prefix();
            out_with_name_helper(args...);
        }

        template<typename T>
        void outg(vector<vector<T>> &g) {
            prefix();
            for(auto& v1 : g){
                for(auto& v2 : v1) {
                    cout << v2 << " ";
                }
                cout << endl;
            }
        }
    };

    template<typename T1, typename... T2>
    void Debug::out_helper(T1 v, T2... args) {
        print(v); cout << endl;
        out_helper(args...);
    }

    template<typename T1, typename... T2>
    void Debug::out_with_name_helper(string s, T1 v, T2... args) {
        cout << s << ": "; print(v); cout << endl;
        out_with_name_helper(args...);
    }

    template<typename T>
    void Debug::print(T val){
        cout << val;
    }

    template<typename A, typename B>
    void Debug::print(pair<A, B> p){
        cout << "("; print(p.first); cout << ", "; print(p.second); cout << ")";
    }

    template<typename A, typename B, typename C>
    void Debug::print(tuple<A, B, C> t) {
        cout << "("; print(get<0>(t)); cout << ", "; print(get<1>(t)); cout << ", "; print(get<2>(t)); cout << ")";
    }

    template<typename T>
    void Debug::print(vector<T>& vec) {
        cout << "[";
        bool fir = true;
        for(auto& e : vec) {
            if(!fir) cout << " ";
            print(e), fir=false;
        }
        cout << "]";
    }

    template<typename T>
    void Debug::print(set<T> &st){
        cout << "{";
        bool fir = true;
        for(auto& e : st) {
            if(!fir) cout << " ";
            print(e), fir=false;
        }
        cout << "}";
    }

    template<typename A, typename B>
    void Debug::print(map<A, B> mp){
        cout << "{";
        bool fir = true;
        for(auto& p : mp){
            if(!fir) cout << " ";
            print(p), fir=false;
        }
        cout << "}";
    }

}

#endif //INCLUDE_DEBUG_HPP

dbg::Debug db;
//</editor-fold>

class BSortingASegment {
public:
	void solve(std::istream& in, std::ostream& out) {
	    int n, k;
	    in >> n >> k;
	    vl a(n);
	    for(int i=0; i<n; i++) in >> a[i];

	    ll ans = 1;
	    queue<int> q;
	    set<int> st;
	    ll mx = 0;
	    for(int i=0; i<n-1; i++){
	        if(q.empty()){
	            q.push(a[i]);
	            st.insert(a[i]);
	            mx = a[i];
	            continue;
	        }
            if(mx > a[i]) ans++;

            if(q.size() == k){
                int p = q.front(); q.pop();
                st.erase(p);
                q.push(a[i]);
                st.insert(a[i]);
            }else{
                q.push(a[i]);
                st.insert(a[i]);
            }
            mx = *(--st.end());
	    }

	    out << ans << endl;
	}
};


int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
	BSortingASegment solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}