Problem: Polycarp is an experienced participant in Codehorses programming contests. Now he wants to become a problemsetter.

He sent to the coordinator a set of n problems. Each problem has it's quality, the quality of the i-th problem is ai (ai can be positive, negative or equal to zero). The problems are ordered by expected difficulty, but the difficulty is not related to the quality in any way. The easiest problem has index 1, the hardest problem has index n.

The coordinator's mood is equal to q now. After reading a problem, the mood changes by it's quality. It means that after the coordinator reads a problem with quality b, the value b is added to his mood. The coordinator always reads problems one by one from the easiest to the hardest, it's impossible to change the order of the problems.

If after reading some problem the coordinator's mood becomes negative, he immediately stops reading and rejects the problemset.

Polycarp wants to remove the minimum number of problems from his problemset to make the coordinator's mood non-negative at any moment of time. Polycarp is not sure about the current coordinator's mood, but he has m guesses "the current coordinator's mood q = bi".

For each of m guesses, find the minimum number of problems Polycarp needs to remove so that the coordinator's mood will always be greater or equal to 0 while he reads problems from the easiest of the remaining problems to the hardest.

Input

The first line of input contains two integers n and m (1 ≤ n ≤ 750, 1 ≤ m ≤ 200 000) — the number of problems in the problemset and the number of guesses about the current coordinator's mood.

The second line of input contains n integers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the qualities of the problems in order of increasing difficulty.

The third line of input contains m integers b1, b2, ..., bm (0 ≤ bi ≤ 1015) — the guesses of the current coordinator's mood q.

Output

Print m lines, in i-th line print single integer — the answer to the problem with q = bi.

Example

Input

6 3
8 -5 -4 1 -7 4
0 7 3


Output

2
0
1

Solution (in JAVA):

Solution:
import javafx.util.Pair;

import java.io.*;
import java.util.*;

public class Main {

    private static myScanner sc;
    private static PrintWriter pw;

    private static final boolean defaultInAndOutPut = true;

    private static final int numberOfTests = 1;

    private static final String nameOfInAndOutFile = "";
    private static final String fullNameInputFile = nameOfInAndOutFile + ".in";
    private static final String fullNameOutputFile = nameOfInAndOutFile + ".out";

    public static void main(String[] args) throws IOException {
        if (defaultInAndOutPut) {
            setDefaultInAndOutPut();
        } else {
            setInAndOutPutFromFile();
        }
        for (int test = 1; test <= numberOfTests; test++) {
            solve();
            pw.flush();
        }

        pw.close();
    }

    private static void setDefaultInAndOutPut() {
        sc = new myScanner(new BufferedReader(new InputStreamReader(System.in)));
        pw = new PrintWriter(System.out);
    }

    private static void setInAndOutPutFromFile() throws IOException {
        sc = new myScanner(new BufferedReader(new FileReader(new File(fullNameInputFile))));
        pw = new PrintWriter(new File(fullNameOutputFile));
    }

    static int n, m;
    static long[] tasks;
    static Pair<Long,Integer>[] questions;

    private static void solve() {
        n = sc.nextInt();
        m = sc.nextInt();
        tasks = new long[n];
        questions = new Pair[m+2];
        for (int i = 0; i < n; i++) tasks[i] = sc.nextLong();
        for (int i = 0; i < m; i++) questions[i] = new Pair<>(sc.nextLong(),i);
        questions[m] = new Pair<>(1000000000000000L,m);
        questions[m+1] = new Pair<>(-1000000000000000L,m+1);
        long[] answers = new long[n + 1];
        Arrays.sort(questions, new Comparator<Pair<Long, Integer>>() {
            @Override
            public int compare(Pair<Long, Integer> o1, Pair<Long, Integer> o2) {
                return Long.compare(o1.getKey(),o2.getKey());
            }
        });

        for (int i = 0; i <= n; i++) {
            answers[i] = getAnsNow(i);
        }
        Arrays.sort(questions, new Comparator<Pair<Long, Integer>>() {
            @Override
            public int compare(Pair<Long, Integer> o1, Pair<Long, Integer> o2) {
                return Integer.compare(o1.getValue(),o2.getValue());
            }
        });
        for (int i = 0; i < m; i++) {
            int min = -1, max = n;
            while (max - min > 1) {
                int mid = (max + min) / 2;
                if (questions[i].getKey() >= answers[mid]) max = mid;
                else min = mid;
            }
            pw.println(max);
        }
    }

    private static int getNumberDeleting(long start) {
        long now = start;
        int c = 0;
        PriorityQueue<Long> set = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            set.add(tasks[i]);
            now += tasks[i];
            if (now < 0) {
                now -= set.poll();
                c++;
            }
        }
        return c;
    }

    private static long getAnsNow(int c) {
        int min = -1;
        int max = m + 1;
        while (max - min > 1) {
            int mid = (max + min) / 2;
            if (getNumberDeleting(questions[mid].getKey()) > c) min = mid;
            else max = mid;
        }
        return questions[max].getKey();
    }
}

class myScanner {
    private char[] buffer = new char[1 << 8];
    private int pos = 1;

    private BufferedReader reader;

    public myScanner(BufferedReader reader) {
        this.reader = reader;
    }

    public boolean hasNext() {
        return pos > 0;
    }

    private void loadBuffer() {
        pos = 0;
        try {
            for (int i; (i = reader.read()) != -1; ) {
                char c = (char) i;
                if (c != ' ' && c != '\n' && c != '\t' && c != '\r' && c != '\f') {
                    if (pos == buffer.length) buffer = Arrays.copyOf(buffer, 2 * pos);
                    buffer[pos++] = c;
                } else if (pos != 0) break;
            }
        } catch (IOException e) {
            throw new UncheckedIOException(e);
        }
    }

    public String current() {
        return String.copyValueOf(buffer, 0, pos);
    }


    public String next() {
        loadBuffer();
        return current();
    }


    public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            throw new UncheckedIOException(e);
        }
    }


    public int nextInt() {
        return nextInt(10);
    }

    public long nextLong() {
        return nextLong(10);
    }

    public int nextInt(int radix) {
        loadBuffer();
        int result = 0;
        int i = buffer[0] == '-' || buffer[0] == '+' ? 1 : 0;
        for (checkValidNumber(pos > i); i < pos; i++) {
            int digit = buffer[i] - '0';
            checkValidNumber(0 <= digit && digit <= radix - 1);
            result = result * radix + digit;
        }
        return buffer[0] == '-' ? -result : result;
    }

    public long nextLong(int radix) {
        loadBuffer();
        long result = 0;
        int i = buffer[0] == '-' || buffer[0] == '+' ? 1 : 0;
        for (checkValidNumber(pos > i); i < pos; i++) {
            int digit = buffer[i] - '0';
            checkValidNumber(0 <= digit && digit <= radix - 1);
            result = result * radix + digit;
        }
        return buffer[0] == '-' ? -result : result;
    }

    public double nextDouble() {
        loadBuffer();
        long result = 0;
        int i = buffer[0] == '-' || buffer[0] == '+' ? 1 : 0;
        long round = 1;
        final int radix = 10;
        boolean hasPoint = false;
        for (checkValidNumber(pos > i); i < pos; i++) {
            int digit = buffer[i] - '0';
            checkValidNumber((0 <= digit && digit <= radix - 1) || (!hasPoint && digit == -2));
            if (digit == -2) hasPoint = true;
            else {
                if (hasPoint) round *= radix;
                result = result * radix + digit;
            }

        }
        return buffer[0] == '-' ? -result / (1.0 * round) : result / (1.0 * round);
    }

    private void checkValidNumber(boolean condition) {
        if (!condition) throw new NumberFormatException(current());
    }
}