Problem:
Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.*
import java.util.*

// N のうち K　のxを訪れる最小歩数
fun solve(N: Int, K: Int, x: IntArray) {
    if (K == 0) {
        println(0)
        return
    }
    val boundary = x.toList().lowerBound(0)
    val negatives = x.slice(0..boundary - 1).asReversed().map { -it.toLong() }
    val positives = x.slice(boundary until N).map { it.toLong() }
    // i だけ negativesからとる
    val INF = 1000000000000L
    var ans = Math.min(
            negatives.getOrElse(K - 1) { INF },
            positives.getOrElse(K - 1) { INF })
    for (i in 1 until K) {
        if (i - 1 >= negatives.size || K - i - 1 >= positives.size || K - i - 1 < 0) continue
        val step1 = 2 * negatives[i - 1] + positives[K - i - 1]
        val step2 = negatives[i - 1] + 2 * positives[K - i - 1]
        ans = Math.min(ans, Math.min(step1, step2))
    }
    println(ans)
    return
}


fun <T : Comparable<T>> List<T?>.lowerBound(
        element: T,
        fromIndex: Int = 0,
        toIndex: Int = size
): Int {
    var low = fromIndex
    var high = toIndex
    while (low < high) {
        val mid = (low + high) / 2
        if (element <= this.get(mid)!!) {
            high = mid
        } else {
            low = mid + 1
        }
    }
    return low
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }

    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }

    val sc = Scanner(System.`in`)
    val N = sc.next().toInt()
    val K = sc.next().toInt()
    val x = IntArray(N)
    for (i in 0 until N) {
        x[i] = sc.next().toInt()
    }
    solve(N, K, x)
}