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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

func main() {
	in := NewInput()
	d := NewData(in)
	d.Run()
}

// Input

type Input struct {
	N int
	K int
	P []int
}

func NewInput() *Input {
	in := Input{}

	fmt.Scan(&in.N)
	fmt.Scan(&in.K)
	in.P = make([]int, in.N)
	for i := 0; i < in.N; i++ {
		fmt.Scan(&in.P[i])
	}

	return &in
}

// Data

type Data struct {
	Num int
}

func NewData(in *Input) *Data {
	d := Data{
		Num: 1,
	}
	if in.N == in.K {
		return &d
	}
	prev := make([]int, in.K)
	curr := make([]int, in.K)
	copy(prev, in.P[0:in.K])
	sort.Ints(prev)
	for i := 1; i < in.N-in.K+1; i++ {
		copy(curr, in.P[i:i+in.K])
		sort.Ints(curr)
		for j := 1; j < in.K; j++ {
			if prev[j] != curr[j-1] {
				d.Num += 1
				break
			}
		}
		copy(prev, curr)
	}
	return &d
}

func (d *Data) Run() {
	d.Output()
}

func (d *Data) Output() {
	fmt.Printf("%d\n", d.Num)
}