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 = Integer.parseInt(sc.next());
        int k = Integer.parseInt(sc.next());
        int[] p = new int[n];
        for(int i=0; i<n; i++){
            p[i] = Integer.parseInt(sc.next());
        }
        
        long ans = 1;
        TreeSet<Integer> a = new TreeSet<>();
        for(int i=0; i<k-1; i++){
            a.add(p[i]);
        }
        
        for(int i=0; i<n-k; i++){
            int first = p[i];
            int last = p[i+k-1];
            a.add(last);
            if(!isAMax(a,last) || !isAMin(a,first)){
                ans++;
            }
            a.remove(p[i]);
        }
        
        System.out.println(Math.max(Math.min(ans, n-k),1));
    }
    
    
    public static boolean isAMax(TreeSet<Integer> a, int x){
        int higher = a.last();
        return higher==x;
    }
    
    public static boolean isAMin(TreeSet<Integer> a, int x){
        int lower = a.first();
        return lower==x;
    }
    
}