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.Collections.Generic;
using System.Linq;
class Program
{
    //static List<string> str = new List<string>();
    static void Main(string[] args)
    {
        // 入力
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        int K = int.Parse(input[1]);
        input = Console.ReadLine().Split(' ');
        List<int> candle = new List<int>();
        for(int i=0; i<N; i++)
        {
            candle.Add(int.Parse(input[i]));
        }

        // 座標0にもっとも近い、正の座標の配列番号を取得する
        int zeroCandle = lower_bound(candle, 0, N-1);

        // 左に移動して、0～K本火をつけてから、右に移動して火をつける・・・をK通り確かめる
        int minDist = -1; // 最小移動距離
        //Console.WriteLine(zeroCandle);
        for (int i = 0; i <= K; i++ )
        {
            //Console.Write(i + " ");
            // 左側でi本、右側で残りに火をつける
            // 左を先につけたときと、右を先につけたとき・・・
            if(zeroCandle - i < 0 || zeroCandle + (K-i-1) >= N)
            {
                // 左か右でろうそくの本数が足りなくなるので
                //Console.WriteLine();
                continue;
            }
            //左にi本付けにいったときの距離
            int left = i == 0 ? 0 : Math.Abs(candle[zeroCandle - i]);
            int right = zeroCandle == N ? 0 : Math.Abs(candle[zeroCandle + (K - i - 1)]);

            // 左を先につけた場合
            int leftFirst = 2 * left + right;
            // 右を先につけた場合
            int rightFirst = left + 2 * right;

            if(minDist < 0 || minDist > Math.Min(leftFirst, rightFirst))
            {
                minDist = Math.Min(leftFirst, rightFirst);
            }

            //Console.WriteLine(leftFirst + " " + rightFirst);
        }

        // 出力
        Console.WriteLine(minDist);
       
    }

    static int lower_bound(List<int> candle, int first, int last)
    {
        if(last - first <= 1)
        {
            if (candle[first] >= 0)
                return first;
            else
                return last;
        }
        // 座標が0にもっとも近い、正の座標を取得する
        if (candle[first] >= 0)
            return first;

        if (candle[last] < 0)
            return last + 1;

        int next = (first + last) / 2;

        //Console.WriteLine("lower_bound:" + first + " " + last + " " + next + " " + candle[next]);

        if (candle[next] > 0)
            return lower_bound(candle, first, next);
        else
            return lower_bound(candle, next, last);


    }
}