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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner();
			int n = cin.Int();
			int k = cin.Int();
			var ms = new List<long>();
			var ps = new List<long>();
			for (int i = 0; i < n; i++) {
				long value = cin.Long();
				if (value == 0) {
					--k;
				} else if (value > 0) {
					ps.Add(value);
				} else {
					ms.Add(value);
				}
			}

			if (k <= 0) {
				Console.WriteLine(0);
				return;
			}

			long ans = 0;
			if (ms.Count == 0) {
				long[] pss = ps.OrderBy(x => x).ToArray();
				ans = pss[k - 1];
			} else if (ps.Count == 0) {
				long[] mss = ms.Select(x => Math.Abs(x)).OrderBy(x => x).ToArray();
				ans = mss[k - 1];
			} else {
				long[] mss = ms.Select(x => Math.Abs(x)).OrderBy(x => x).ToArray();
				long[] pss = ps.OrderBy(x => x).ToArray();

				int mn = mss.Length;
				int pn = pss.Length;

				long min = (mss[mn - 1] + pss[pn - 1]) * 2;
				for (int i = 0; i < mn; i++) {
					int remain = k - i - 1;
					if (remain > 0 && remain <= pn) {
						long temp = mss[i] * 2 + pss[remain - 1];
						min = Math.Min(temp, min);
					}
				}

				for (int i = 0; i < pn; i++) {
					int remain = k - i - 1;
					if (remain > 0 && remain <= mn) {
						long temp = pss[i] * 2 + mss[remain - 1];
						min = Math.Min(temp, min);
					}
				}

				if (pn >= k) {
					long temp = pss[k - 1];
					min = Math.Min(temp, min);
				}

				if (mn >= k) {
					long temp = mss[k - 1];
					min = Math.Min(temp, min);
				}

				ans = min;
			}

			Console.WriteLine(ans);
		}
	}

	public class Scanner
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private string[] buf_;
		private int index_;

		public Scanner()
		{
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = Console.ReadLine();
			while (st == "") {
				st = Console.ReadLine();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}
	}
}