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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		//List<String> list= new ArrayList<String>(Arrays.asList(s.split("")));
		//List<Integer> list_gold=new ArrayList<Integer>();
		//Integer[] Republican = new Integer[m];
		//List<Integer> list=new ArrayList<Integer>();
		List<Integer> list=new ArrayList<Integer>();
		List<Integer> list_up=new ArrayList<Integer>();

		int n = sc.nextInt();
		int k = sc.nextInt();

		for(int i=0;n>i;i++) {
			int a = sc.nextInt();
			list.add(a);
			list_up.add(a);
		}

		Collections.sort(list_up);
		int count=0;

		for(int i=0;n>i;i++) {
			if(!list.get(i).equals(list_up.get(i))) {
				count++;
			}
			if(n-i>=k) {
				for(int j=0;k>j;j++) {
					if(list.get(i+j).equals(list_up.get(i+j))) {
						break;
					}
					if(j==k-1) {
						count--;
					}
				}
			}
		}
		if(count==0) {
			System.out.println(1);
		}

		else {
			System.out.println(count);
		}


	}

}