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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <utility>
#include <numeric>
#include <array>
#include <cmath>
#include <memory>
#include <map>
#include <set>
using namespace std;
//変数デバッグ
#define DEB(variable) cout << #variable << '=' << variable << endl

//for簡易表記(引数ミス防止)
#define FOR(LoopVariable,numberOFbegin,numberOFend) for (long long int LoopVariable = (numberOFbegin); (LoopVariable) < (numberOFend); (LoopVariable)++)
#define DEFOR(LoopVariable,numberOFbegin,numberOFend) for (long long int LoopVariable = (numberOFbegin)-1; (LoopVariable) >= (numberOFend); (LoopVariable)--)
#define REP(LoopVariable,numberOFend) for(long long int LoopVariable = 0;(LoopVariable)<(numberOFend);LoopVariable++)

constexpr long long int linf = numeric_limits<long long int>::max()-5;
constexpr int inf= numeric_limits<int>::max()-5;
constexpr long long int mod = 1000000007;

int main(){

    long long int n,k;
    cin >> n >> k;
    vector<long long int> v(n);
    REP(i,n){
        scanf("%lld",&v[i]);
    }
    vector<long long int> tmp(n);
    set < vector<long long int>> st;
    REP(i,n-k+1){
        tmp = v;
        sort(tmp.begin() + i, tmp.begin() + i + k);
        st.insert(tmp);
    }
    cout << st.size() << endl;



    return 0;
}