Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day i he will make a pile of snow of volume Vi and put it in her garden.

Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is Ti, each pile will reduce its volume by Ti. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other. 

Note that the pile made on day i already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.

You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day. 

Input

The first line contains a single integer N (1 ≤ N ≤ 105) — the number of days. 

The second line contains N integers V1, V2, ..., VN (0 ≤ Vi ≤ 109), where Vi is the initial size of a snow pile made on the day i.

The third line contains N integers T1, T2, ..., TN (0 ≤ Ti ≤ 109), where Ti is the temperature on the day i.

Output

Output a single line with N integers, where the i-th integer represents the total volume of snow melted on day i.

Examples

Input

3
10 10 5
5 7 2


Output

5 12 4


Input

5
30 25 20 15 10
9 10 12 4 13


Output

9 20 35 11 25

Note

In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day.
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.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cacophonix
 */
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);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            Thread t = new Thread(null, new Run(in, out), "name", 1 << 28);
            t.start();
            try {
                t.join();
            } catch (InterruptedException e) {

            }
        }

        public class Run extends Thread {
            InputReader in;
            OutputWriter out;

            public Run(InputReader in, OutputWriter out) {
                this.in = in;
                this.out = out;
            }

            int upper_bound(long val, long[] arr) {
                int lo = 0;
                int hi = arr.length;
                int mid;
                while (lo < hi) {
                    mid = (lo + hi) >> 1;

                    if (val < arr[mid]) {
                        hi = mid;
                    } else {
                        lo = mid + 1;
                    }
                }
                return lo;
            }


            public void run() {
                int N = in.readInt();
                long[] t = new long[N + 2];
                long[] cumt = new long[N + 2];
                long[] ans = new long[N + 2];
                long[] v = new long[N + 1];

                //long[] arr = {1,2,2,3};
                //out.printLine(upper_bound(2,arr));

                for (int i = 0; i < N; i++) {
                    v[i] = in.readLong();
                }

                for (int i = 0; i < N; i++) {
                    t[i + 1] = in.readLong();
                    cumt[i + 1] = t[i + 1];
                    cumt[i + 1] += cumt[i];
                }
                cumt[N + 1] = cumt[N] + Integer.MAX_VALUE;

                FenwickTree complete = new FenwickTree(N * 2);

                //out.printLine(cumt);

                for (int i = 0; i < N; i++) {
                    //if(v[i]==0)continue;
                    int id = upper_bound(v[i] + cumt[i], cumt);

                    complete.add(i + 1, 1);
                    complete.add(id, -1);
                    //out.printLine(id,v[i]+cumt[i],v[i]+cumt[i]-cumt[id-1]+"#");
                    ans[id] += v[i] + cumt[i] - cumt[id - 1];
                }

                for (int i = 1; i <= N; i++) {
                    //out.printLine(complete.get(1,i));
                    out.print((complete.get(1, i) * t[i] + ans[i]) + " ");
                }
            }

        }

    }

    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 print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

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

    }

    static class FenwickTree {
        private final long[] value;

        public FenwickTree(int size) {
            value = new long[size];
        }

        public long get(int from, int to) {
            return get(to) - get(from - 1);
        }

        private long get(int to) {
            to = Math.min(to, value.length - 1);
            long result = 0;
            while (to >= 0) {
                result += value[to];
                to = (to & (to + 1)) - 1;
            }
            return result;
        }

        public void add(int at, long value) {
            while (at < this.value.length) {
                this.value[at] += value;
                at = at | (at + 1);
            }
        }

    }

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

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

        }

    }
}

