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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int K = sc.nextInt();
        int[] P = new int[N];
        for(int i=0; i<N; i++)
            P[i] = sc.nextInt();

        int ans = 1;
        TreeSet<Integer> ts = new TreeSet<>();
        for(int i=0; i<N; i++) {
            ts.add(P[i]);
            if(i>=K) {
                if(ts.last()!=P[i] || ts.first()!=P[i-K]) {
                    ans++;
                }
                ts.remove(P[i-K]);
            }
        }
//        System.out.println(ts);

        int notChange=0;
        int cnt=1;
//        for(int i=1; i<N; i++) {
//            if(P[i-1]<P[i]) {
//                cnt++;
//                if(cnt==K)
//                    notChange++;
//            } else {
//                cnt=1;
//            }
//        }

        System.out.println(ans - (notChange>=2 ? notChange-1 : 0));
        sc.close();
    }
}