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) = readInputLine().split(" ").map{it.toInt()}
    
    val xs = readInputLine().split(" ").map{it.toInt()}.toIntArray()
    
    var l = 0
    var r = K - 1
    
    var ans = distance(xs, l, r)

    while (r < N - 1) {
        val nextDistance = distance(xs, l + 1, r + 1)
        if (nextDistance < ans) {
            ans = nextDistance
            l++
            r++
        }
        if (xs[l + 1] > 0) {
            break
        }
    }
    
    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}

fun distance(xs: IntArray, l: Int, r: Int): Int {
    return if (xs[l] <= 0 && xs[r] <= 0) -xs[l] else if (xs[l] >= 0 && xs[r] >= 0) xs[r] else xs[r] - xs[l] * 2
}