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)

fun main(args: Array<String>) {
    val pw = java.io.PrintWriter(System.out)
    Problem.solve(java.util.Scanner(System.`in`), pw)
    pw.flush()
}

object Problem {
    lateinit var dfs: (v: Int, p: Int) -> Unit

    fun solve(sc: java.util.Scanner, pw: java.io.PrintWriter) {
        val N = sc.next().toInt()
        val K = sc.next().toInt()
        val x = Array(N) { sc.next().toLong() }
        val xl = listOf(0L) + x.filter { it < 0 }.map { -it }.sorted().take(K)
        val xr = listOf(0L) + x.filter { it >= 0 }.take(K)
        val ans = mutableListOf<Long>()
        for (i in 0..K) {
            if (i < xr.count() && K - i < xl.count()) {
                val a1 = xl[K - i]
                val a2 = xr[i]
                ans += a1 * 2 + a2
                ans += a1 + a2 * 2
            }
        }
        pw.println(ans.min()!!)
    }
}