Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

Input Format

N K
a_1 a_2 a_3 ... a_N

Output Format

Print the minimum cost in one line. In the end put a line break.

Constraints

1 ≤ K ≤ N ≤ 15

1 ≤ a_i ≤ 10^9

Scoring

Subtask 1 [120 points]

N = K

Subtask 2 [90 points]

N ≤ 5

a_i ≤ 7

Subtask 3 [140 points]

There are no additional constraints.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 1000005), 1000005)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}

func getNextUint64(scanner *bufio.Scanner) uint64 {
	i, _ := strconv.ParseUint(getNextString(scanner), 10, 64)
	return i
}

func getNextFloat64(scanner *bufio.Scanner) float64 {
	i, _ := strconv.ParseFloat(getNextString(scanner), 64)
	return i
}

func main() {
	fp := os.Stdin
	wfp := os.Stdout
	cnt := 0

	if os.Getenv("MASPY") == "ますピ" {
		fp, _ = os.Open(os.Getenv("BEET_THE_HARMONY_OF_PERFECT"))
		cnt = 1
	}
	if os.Getenv("MASPYPY") == "ますピッピ" {
		wfp, _ = os.Create(os.Getenv("NGTKANA_IS_GENIUS10"))
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(wfp)
	solve(scanner, writer)
	for i := 0; i < cnt; i++ {
		fmt.Fprintln(writer, "-----------------------------------")
		solve(scanner, writer)
	}
	writer.Flush()
}

func solve(scanner *bufio.Scanner, writer *bufio.Writer) {
	n := getNextInt(scanner)
	k := getNextInt(scanner)
	aa := make([]int, n)
	mm := make([]int, n+1)
	for i := 0; i < n; i++ {
		aa[i] = getNextInt(scanner)
		if mm[i] > aa[i] {
			mm[i+1] = mm[i]
			continue
		}
		mm[i+1] = aa[i]
	}

	var ans, s int64
	ans = math.MaxInt64
	for b := 0; b < 1<<uint(n); b++ {
		sum := 0
		m := 0
		for i := 0; i < n; i++ {
			sum += b >> uint(i) & 1
		}
		if sum < k {
			continue
		}
		s = 0
		for i := 0; i < n; i++ {
			if b>>uint(i)&1 == 0 {
				continue
			}
			m = maxint(m, mm[i])
			if aa[i] < m+1 {
				s += int64(m + 1 - aa[i])
			}
			m = maxint(aa[i], m+1)
		}
		if ans > s {
			ans = s
		}
	}
	fmt.Fprintln(writer, ans)
}

func maxint(a, b int) int {
	if a < b {
		return b
	}
	return a
}