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.Linq.Expressions;
using System.IO;
using System.Text;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const int M2 = 998244353;
    const long LM = (long)1e18;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    const string dstring = "RDLU";
    static void Main()
    {
        int n, q;
        sc.Multi(out n, out q);
        var a = sc.IntArr;
        var ims = new long[n + 1];
        var evims = new long[n + 1];
        var odims = new long[n + 1];
        for (int i = 0; i < n; i++)
        {
            ims[i + 1] = ims[i] + a[i];
            evims[i + 1] = evims[i];
            odims[i + 1] = odims[i];
            if (i % 2 == 0)
                evims[i + 1] += a[i];
            else
                odims[i + 1] += a[i];
        }
        for (int _ = 0; _ < q; _++)
        {
            int x = sc.Int;
            if (Math.Abs(x - a[n - 1]) < Math.Abs(x - a[n - 2])) {
                if (n % 2 == 0) {
                    Prt(odims[n]);
                }
                else
                    Prt(evims[n]);
                continue;
            }
            int ok = 0, ng = M;
            while (ok < ng - 1) {
                int m = (ok + ng) / 2;
                int j1 = a.LowerBound(x - m);
                int j2 = a.UpperBound(x + m) - 1;
                int c = j2 - j1 + 1;
                if (j2 + c >= n) {
                    ng = m;
                }
                else {
                    ok = m;
                }
            }
            {
                int j1 = a.LowerBound(x - ok);
                int j2 = a.UpperBound(x + ok) - 1;
                int c = j2 - j1 + 1;
                int rc = n - j2 - 1 - c;
                if (rc < 0 || rc > 2) throw new Exception();
                long ret = ims[n] - ims[n - c];
                int l = j1 - 1, r = j2 + 1;
                int p = n - c - 1;
                while (r <= p) {
                    ret += a[p];
                    --p;
                    --rc;
                    if (l < 0 && r > p) break;
                    if (l >= 0 && r <= p) {
                        if (Math.Abs(x - a[l]) <= Math.Abs(x - a[r])) {
                            --l;
                        }
                        else
                            ++r;
                    }
                    else if (l >= 0) {
                        --l;
                    }
                    else {
                        ++r;
                    }
                }
                if (l % 2 == 0) {
                    ret += evims[l + 1];
                }
                else {
                    ret += odims[l + 1];
                }
                Prt(ret);
            }
        }
        sw.Flush();
    }

    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) {
        a = v1; b = v2;
    }
    public static bool operator>(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) > 0;
    public static bool operator<(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) < 0;
    public static bool operator>=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) >= 0;
    public static bool operator<=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) <= 0;
}
static class util
{
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static T sq<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan
{
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => Console.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P {
        get {
            int a, b;
            Multi(out a, out b);
            return new P(a, b);
        }
    }
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}

static class Search
{
    // x より大きいの項の index のうち最小のものを返す
    // x 以下の項の index のうち最大のもの + 1 を返す
    // そこに挿入
    public static int UpperBound<T>(this IList<T> a, T x) where T : IComparable<T> {
        int le = -1, u = a.Count;
        while (le < u - 1) {
            int m = (le + u) >> 1;
            if (a[m].CompareTo(x) > 0) u = m;
            else le = m;
        }
        return le + 1;
    }
    public static int UpperBound<T>(this IList<T> a, T x, Func<T, T, int> compare) {
        int le = -1, u = a.Count;
        while (le < u - 1) {
            int m = (le + u) >> 1;
            if (compare(a[m], x) > 0) u = m;
            else le = m;
        }
        return le + 1;
    }

    // n 未満の項の index のうち最大のもの + 1 を返す
    // n 以上の項の index のうち最小のものを返す
    // そこに挿入
    public static int LowerBound<T>(this IList<T> a, T x) where T : IComparable<T> {
        int l = -1, ue = a.Count;
        while (l < ue - 1) {
            int m = (l + ue) >> 1;
            if (a[m].CompareTo(x) < 0) l = m;
            else ue = m;
        }
        return ue;
    }
    public static int LowerBound<T>(this IList<T> a, T x, Func<T, T, int> compare) {
        int l = -1, ue = a.Count;
        while (l < ue - 1) {
            int m = (l + ue) >> 1;
            if (compare(a[m], x) < 0) l = m;
            else ue = m;
        }
        return ue;
    }
}