Problem:
Score : 500 points

Problem Statement

There are N cards. The i-th card has an integer A_i written on it.
For any two cards, the integers on those cards are different.

Using these cards, Takahashi and Aoki will play the following game:

Aoki chooses an integer x.

Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner:

Takahashi should take the card with the largest integer among the remaining card.

Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards.

The game ends when there is no card remaining.

You are given Q candidates for the value of x: X_1, X_2, ..., X_Q.
For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i.

Constraints

2 \leq N \leq 100 000

1 \leq Q \leq 100 000

1 \leq A_1 < A_2 < ... < A_N \leq 10^9

1 \leq X_i \leq 10^9 (1 \leq i \leq Q)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 ... A_N
X_1
X_2
:
X_Q

Output

Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i.

Sample Input 1

5 5
3 5 7 11 13
1
4
9
10
13

Sample Output 1

31
31
27
23
23

For example, when x = X_3(= 9), the game proceeds as follows:

Takahashi takes the card with 13.

Aoki takes the card with 7.

Takahashi takes the card with 11.

Aoki takes the card with 5.

Takahashi takes the card with 3.

Thus, 13 + 11 + 3 = 27 should be printed on the third line.

Sample Input 2

4 3
10 20 30 40
2
34
34

Sample Output 2

70
60
60

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace ConsoleAppNearestCardGame0123
{
    class Program
    {
        public struct members
        {
            public int distance;
            public int Aoki;
        }
        static void Main(string[] args)
        {
            // 整数の入力
            //int n = int.Parse(Console.ReadLine());
            // スペース区切りの整数の入力
            //string[] input = Console.ReadLine().Split(' ');
            //int b = int.Parse(input[0]);
            //int c = int.Parse(input[1]);
            // 文字列の入力
            //string s = Console.ReadLine();
            var inputNQ = Console.ReadLine().Split().Select(int.Parse).ToArray();// N枚数、Q種類の候補
            var inputA = Console.ReadLine().Split().Select(int.Parse).ToArray();// N枚のカードの値
                                                                                //List<int> X = new List<int>();

            int N = inputNQ[0];
            int Q = inputNQ[1];
            int[] X = new int[Q];


            for (int i = 0; i < Q; i++) // Qは候補の数
            {
                X[i] = int.Parse(Console.ReadLine());// 指定する値
            }
            //
            // 入力終わり
            //

            // ソートする前のオリジナルのカード情報を保持
            var father = new int[N];
            Array.Copy(inputA,father,inputA.Length);

            Array.Reverse(inputA);// 大きい順にソートした。高橋くんの取るカードの順序
            int[] distance = new int[N];// 配列の宣言
            int distanceFromX = 0;
            List<members> distanceList = new List<members>();

            List<int> CheckList = new List<int>();
            for (int j = 0; j < X.Length; j++) // 指定された値
            {
                //
                // ショートカット１
                //
                double short_ans = 0;
                if (N > 3)//カードの枚数が３以上で、端っこに指定の数かあるとき
                {
                    float f1_point = (father[N - 3] + father[N - 2]) / 2;
                    if (X[j] > f1_point)
                    {
                        for (int j2 = 0; j2 < N; j2++)
                        {
                            if (j2 % 2 == 0)
                            {
                                short_ans += inputA[j2];
                            }
                        }
                        //Console.WriteLine("ショートカット１しました");
                        Console.WriteLine(short_ans);
                        continue;
                    }
                }
                //
                // ショートカット２
                //
                if ((N >= 4) && (N % 2 == 0) && (X[j] <=father[ (N + 6) / 4])) // カードの枚数が偶数で指定の数が小さいとき
                {
                    for (int j3 = 0; j3 < N / 2; j3++)
                    {
                        short_ans += father[N - j3 - 1];
                    }
                    //Console.WriteLine("ショートカット２しました");
                    Console.WriteLine(short_ans);
                    continue;
                }
                //
                // ショートカット３
                //
                if ((N >= 3) && (N % 2 == 1) && (X[j] <= father[(N + 3) / 4])){ // カードの枚数が奇数で指定の数が小さいとき
                    for(int j4=0;j4 <= N/2; j4++)
                    {
                        short_ans += father[N - j4-1];
                    }
                        //Console.WriteLine("ショートカット３しました");
                    Console.WriteLine(short_ans);
                    continue;
                }
                //
                distanceList.Clear();
                CheckList.Clear();

                for (int i = 0; i < N; i++)
                {
                    members ms;
                    distanceFromX = X[j] - inputA[i];//指定されたx[j]からの距離（同じ距離なら小さい方を選ぶ）
                    ms.distance = Math.Abs(distanceFromX);
                    ms.Aoki = inputA[i];
                    distanceList.Add(ms);
                }
                // 指定されたx[j]からの距離順にソートして値の小さいものを優先し、新しいリストに記録する。
                var dL = distanceList.OrderBy(a => a.distance).ThenBy(a => a.Aoki).ToList();

                int onlyTakahashi = 0;


                CheckList.Clear();
                for (int k = 0; k < N; k++)
                {
                    if (CheckList.Contains(inputA[k]) == false)
                    {
                        CheckList.Add(inputA[k]);// 高橋くんの取るカード
                    }
                    else
                    {
                        break;
                    }
                    if (CheckList.Contains(dL[k].Aoki) == false)
                    {
                        CheckList.Add(dL[k].Aoki);
                    }
                    else
                    {
                        break;
                    }
                }
                onlyTakahashi = (CheckList.Count + 1) / 2;// 高橋くんだけが取る個数（大きい方から）

                double ans = 0;
                for (int m = 0; m < onlyTakahashi; m++)
                {
                    ans += inputA[m];
                }
                for (int n = onlyTakahashi * 2; n < inputA.Length; n++)
                {
                    if (n % 2 == 0)
                    {
                        ans += inputA[n];
                    }
                }
                /*
                Console.Write(X[j]+"  ");
                foreach (var member in dL)
                {
                    Console.Write(member.Aoki + " ");
                }
                */
                Console.WriteLine(ans);

                /*
                Console.Write(X[j] + "によって並べ替えたinputAの値:");
                foreach (var member in distanceList)
                {
                    Console.Write(member.Aoki + " ");
                }
                Console.WriteLine();
                */
                //Console.WriteLine("高橋くんだけが取る："+onlyTakahashi);
                
            }
        }// Main終わり
    }
}