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: Time Limit Exceeded)

fun main(args: Array<String>) {
    val (n, k) = readLine()!!.split(" ").map { it.toInt() }
    val xs = readLine()!!.split(" ").map { it.toInt() }
    val minusXs = xs.filter { x -> x < 0 }.sortedDescending()
    val plusXs = xs.minus(minusXs)
    var minusSum = 0
    var plusSum = 0
    var mi = 0
    var pi = 0

    for (j in 0 until k) {
        if (mi >= minusXs.size) {
            plusSum = plusXs[k - mi - 1]
            break
        }
        if (pi >= plusXs.size){
            minusSum = minusXs[k - pi - 1]
            break
        }
        if (-minusXs[mi] < plusXs[pi]) {
            minusSum += minusXs[mi] - minusSum
            mi++
        } else {
            plusSum += plusXs[pi] - plusSum
            pi++
        }
    }
    if (-minusSum < plusSum)
        println("${-minusSum * 2 + plusSum}")
    else
        println("${plusSum * 2 + -minusSum}")
}