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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var nk = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var n = nk[0];
        var k = nk[1];
        var xs = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

        k -= 1;
        var shortest = long.MaxValue;
        int i = k;
        while (i < n && xs[i] < 0)
        {
            shortest = -xs[i - k];
            i++;
        }
        while (i < n && xs[i - k] < 0)
        {
            var s = -xs[i - k];
            var l = xs[i];
            if (s > l)
            {
                var t = s;
                s = l;
                l = t;
            }
            shortest = Math.Min(shortest, s * 2 + l);
            i++;
        }
        if (i < n && xs[i] < shortest)
        {
            shortest = xs[i];
        }
        Console.WriteLine(shortest);
    }
}