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: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func nextIntLine() []int {
	sc.Scan()
	splitStr := strings.Fields(sc.Text())
	ints := make([]int, len(splitStr))
	for i := 0; i < len(splitStr); i++ {
		n, _ := strconv.Atoi(splitStr[i])
		ints[i] = n
	}
	return ints
}

func main() {
	nk := nextIntLine()
	n, k := nk[0], nk[1]
	nums := nextIntLine()
	countMap := map[string]struct{}{}
	for i := 0; i < n-k+1; i++ {
		_nums := make([]int, len(nums))
		copy(_nums, nums)
		tmp := _nums[i : i+k]
		sort.Ints(tmp)
		var s string
		for j := 0; j < n; j++ {
			if i <= j && j < i+k {
				s += fmt.Sprintf("%d", tmp[j-i])
			} else {
				s += fmt.Sprintf("%d", nums[j])
			}
		}
		countMap[s] = struct{}{}
	}
	fmt.Println(len(countMap))
}