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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Random;
import java.util.Set;
import java.util.TreeSet;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/A1";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        /*
        int[] s = new int[101];
        Random r = new Random();
        for (int i = 0; i < 101; i++) {
            s[i] = r.nextInt(10000);
        }
        Arrays.sort(s);
        for (int i = 0; i < 101; i++) {
            System.out.print(s[i] + " ");
        }
        */
        int N = in.nextInt(), Q = in.nextInt();
        int[] a = in.nextIntArray(N);
        int[] X = in.nextIntArray(Q);

        long[] v = new long[(N+1)/2];
        long[] sum = new long[(N+1)/2+1];
        for (int i = N - 1; i >= N / 2; i--) {
            sum[0] += a[i];
        }
        for (int ptr = 0, i = N / 2, j = N % 2 == 0 ? 1 : 0; i < N; ptr++, i++, j += 2) {
            v[ptr] = a[j] + (a[i] - a[j]) / 2 + 1;
            sum[ptr+1] = sum[ptr] - (a[i] - a[j]);
            // System.out.println(v[ptr] + " " + sum[ptr+1]);
        }

        for (int i = 0; i < Q; i++) {
            int lo = -1, hi = v.length;
            while (hi - lo > 1) {
                int mid = (hi + lo) / 2;
                if (v[mid] < X[i] + 1) {
                    lo = mid;
                } else {
                    hi = mid;
                }
            }
            System.out.println(sum[lo+1]);
        }

        /*
        Set<List<Integer>> hash = new TreeSet<>((l1, l2) -> {
            for (int i = 0; i < l1.size(); i++) {
                if (l1.get(i) > l2.get(i)) {
                    return 1;
                } else if (l1.get(i) < l2.get(i)) {
                    return -1;
                }
            }
            return 0;
        });
        for (int i = 0; i < 10000; i++) {
            naive(a, i, hash);
        }
        */
    }

    private void naive(int[] a, int x, Set<List<Integer>> set) {
        int n = a.length;
        boolean[] used = new boolean[n];

        int turn = 0;
        List<Integer> takahashi = new ArrayList<>();
        List<Integer> aoki = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int nextIdx = -1;
            List<Integer> l = turn == 0 ? takahashi : aoki;
            for (int j = 0; j < n; j++) {
                if (!used[j]) {
                    if ((nextIdx == -1 && !used[j]) || (turn == 0 && a[nextIdx] < a[j]) || (turn == 1 && Math.abs(a[nextIdx] - x) > Math.abs(a[j] - x))) {
                        nextIdx = j;
                    }
                }
            }
            used[nextIdx] = true;
            l.add(nextIdx);
            turn ^= 1;
        }
        // System.out.println(x + " : " + takahashi + " " + aoki + " " + takahashi.stream().reduce(0, (i1, i2) -> i1 + i2));
        if (!set.contains(takahashi)) {
            System.out.println(x + " " + takahashi + " " + takahashi.stream().reduce(0, (i1, i2) -> i1 + a[i2]));
        }
        set.add(takahashi);
    }

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                // TODO 自動生成された catch ブロック
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }

    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
            // stream = new FileInputStream(new File("dec.in"));

        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}