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.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int[] V = new int[N];
            for (int i = 0; i < N; i++) V[i] = in.nextInt();
            int[] T = new int[N];
            for (int i = 0; i < N; i++) T[i] = in.nextInt();
            long[] Tsum = new long[N + 1];
            for (int i = 1; i <= N; i++) Tsum[i] = Tsum[i - 1] + (long) T[i - 1];
            int[] fullVNder = new int[N];
            long[] fullVNrem = new long[N];
            for (int i = 0; i < N; i++) {
                fullVNder[i]++;
                long fullDesPar = Tsum[i] + V[i];
                int r = N;
                int l = 0;
                while (r - l > 1) {
                    if (Tsum[(l + r) / 2] >= fullDesPar) {
                        r = (l + r) / 2;
                    } else {
                        l = (l + r) / 2;
                    }
                }
                if (Tsum[r] >= fullDesPar) {
                    int lastDay = r - 1;
                    fullVNder[lastDay]--;
                    fullVNrem[lastDay] += V[i] - Tsum[lastDay] + Tsum[i];
                }
            }
            int[] fullVNinteg = new int[N];
            fullVNinteg[0] = fullVNder[0];
            for (int i = 1; i < N; i++) {
                fullVNinteg[i] = fullVNinteg[i - 1] + fullVNder[i];
            }
            for (int i = 0; i < N; i++) {
                out.print(((long) fullVNinteg[i] * (long) T[i] + fullVNrem[i]) + " ");
            }
        }

    }

    static class InputReader {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private void fillTokenizer() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            fillTokenizer();
            return tokenizer.nextToken();
        }

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

    }
}

