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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
//using System.Text;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;
//using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    void chmax<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? b : a; }
    void chmin<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? a : b; }

    void solve()
    {
        int N = cin.nextint;
        int Q = cin.nextint;

        var A = new long[N + 1];

        for (int i = 0; i < N; i++)
        {
            A[i] = cin.nextint;
        }
        Array.Reverse(A);
        var KOUGO = new long[N + 1];
        for (int i = N; i >= 0; i--)
        {
            if (i != N)
            {
                KOUGO[i] = KOUGO[i + 1];
            }
            if (i % 2 == 1)
            {
                KOUGO[i] += A[i];
            }
        }
        long TAKESUM = 0;
        //bool flag = true;
        int S = 1;

        var L = new List<long>(); //境界をおいておく
        var R = new List<long>(); //答えをおいておく
        while (true)
        {
            TAKESUM += A[S];
            int WANT = S + 1;
            int KOUGOSTART = 2 * S + 1;
            if (KOUGOSTART > N)
            {
                L.Add(0);//0以上ならそうなる
                R.Add(TAKESUM);
                break;
            }
            var C = (A[WANT] + A[KOUGOSTART]) / 2 + 1;
            L.Add(C);
            R.Add(TAKESUM + KOUGO[KOUGOSTART]);
            S++;
        }

        L.Reverse();
        R.Reverse();
        //cin.join(L);
        //cin.join(R);


        for (int i = 0; i < Q; i++)
        {
            var x = cin.nextlong;
            int idx = upper_bound(L, x) - 1;
            WriteLine(R[idx]);
        }
    }

    int upper_bound(List<long> arr, long val)
    {
        int low = 0, high = arr.Count();
        int mid;

        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid] <= val) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    int lower_bound(int[] arr, int val)
    {
        int low = 0, high = arr.Count();
        int mid;

        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid] < val) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
    public void join<T>(IEnumerable<T> values) { WriteLine(string.Join(" ", values)); }
}