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.Scanner;
import java.util.TreeSet;

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

    int N = scanner.nextInt();
    int K = scanner.nextInt();
    int[] p = new int[N];
    int[] cummDelta = new int[N + 1];
    for (int i = 0; i < N; i++) p[i] = scanner.nextInt();
    for (int i = 1; i < N; i++) cummDelta[i] = cummDelta[i - 1] + (p[i] > p[i - 1] ? 1 : 0);

    int count = N - K + 1;
    for (int i = 0; i < N - K; i++) if (cummDelta[i + K - 1] - cummDelta[i] == K - 1) count--;

    TreeSet<Integer> set = new TreeSet<>();
    for (int i = 0; i < K; i++) set.add(p[i]);

    for (int i = 0; i < N - K; i++) {
      set.remove(p[i]);
      if (p[i] <= set.first() && p[i + K] >= set.last()) count--;
      set.add(p[i + K]);
    }
    System.out.println(count);
  }
}