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: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DNearestCardGame solver = new DNearestCardGame();
        solver.solve(1, in, out);
        out.close();
    }

    static class DNearestCardGame {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            int q = in.nextInt();

            long[] a = in.nextLongArray(n);

            int[] x = in.nextIntArray(q);

            long[][] dp = new long[n][2];

            dp[0][0] = a[0];

            for (int i = 1; i < n; i++) {
                //0
                dp[i][0] = a[i] + dp[i - 1][1];

                //1
                dp[i][1] = dp[i - 1][0];
            }

            long[] suf = in.calculateSuffixSum(a);

            for (int i = 0; i < q; i++) {
                int cx = x[i];

                if (cx >= a[n - 1]) {
                    out.println(dp[n - 1][0]);
                    continue;
                }

                int lo = fig(cx, a, n);
                int hi = n - 1;

                int ans = n - 1;

                int ftcnt = 1;
                int facnt = 0;
                while (lo <= hi) {
                    int mid = (lo + hi) / 2;

                    int tcnt = n - mid;

                    int acnt;

                    if (mid > 0) {
                        long diff = a[mid] - cx;
                        long cxm = cx - diff;

                        int fig = fig(cxm - 1, a, n);

                        acnt = mid - fig;
                    } else {
                        acnt = 0;
                    }

                    if (tcnt > acnt + 1) {
                        lo = mid + 1;
                    } else if (tcnt < acnt) {
                        if (mid < ans) {
                            ftcnt = tcnt;
                            facnt = acnt;
                            ans = Math.min(ans, mid);
                        }
                        hi = mid - 1;
                    } else {
                        if (mid < ans) {
                            ftcnt = tcnt;
                            facnt = acnt;
                            ans = Math.min(ans, mid);
                        }
                        hi = mid - 1;
                    }
                }

                if (ftcnt > facnt) {
                    int li = n - 1 - ftcnt - facnt;

                    if (li < 0)
                        out.println(suf[n - ftcnt]);
                    else {
                        out.println(suf[n - ftcnt] + dp[li][1]);
                    }
                } else {
                    int li = n - 1 - ftcnt - facnt;

                    if (li < 0)
                        out.println(suf[n - ftcnt]);
                    else {
                        out.println(suf[n - ftcnt] + dp[li][0]);
                    }
                }

            }
        }

        int fig(long num, long[] a, int n) {
            int lo = 0;
            int hi = n - 1;

            int ans = n;
            while (lo <= hi) {
                int mid = (lo + hi) / 2;

                if (a[mid] > num) {
                    ans = mid;
                    hi = mid - 1;
                } else {
                    lo = mid + 1;
                }
            }

            return ans;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

        public 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++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

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

        public long[] calculateSuffixSum(long[] a) {
            int n = a.length;

            long[] suffixSum = new long[n];

            suffixSum[n - 1] = a[n - 1];

            for (int i = n - 2; i >= 0; i--) {
                suffixSum[i] = suffixSum[i + 1] + a[i];
            }

            return suffixSum;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}