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.*;
import java.util.*;

public class C {

    MyScanner in;
    PrintWriter out;

    public static void main(String[] args) throws Exception {
        new C().run();
    }

    public void run() throws Exception {
        in = new MyScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    static class Pile {
        int day;
        int size;

        public Pile(int day, int size) {
            this.day = day;
            this.size = size;
        }
    }

    static class Event implements Comparable<Event> {
        int type; // 0 appears, 1 melts
        int day;
        Pile pile;

        @Override
        public int compareTo(Event o) {
            if (day != o.day) {
                return day - o.day;
            }
            return type - o.type;
        }

        public Event(int type, int day, Pile pile) {
            this.type = type;
            this.day = day;
            this.pile = pile;
        }
    }

    int upperBound(long x, long[] a) {
        int n = a.length;
        int l = -1, r = n;

        while (r - l > 1) {
            int m = (l + r) / 2;
            if (a[m] < x) {
                l = m;
            } else {
                r = m;
            }
        }

        return r;
    }

    public void solve() throws Exception {
        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[] acct = new long[n];

        for (int i = 0; i < n; i++) {
            acct[i] = ((i == 0) ? 0L : acct[i - 1]) + t[i];
        }

        ArrayList<Event> events = new ArrayList<Event>();

        for (int i = 0; i < n; i++) {
            Pile pile = new Pile(i, v[i]);
            events.add(new Event(0, i, pile));
            int meltDay = upperBound(((i == 0) ? 0L : acct[i - 1]) + v[i], acct);
            if (meltDay != n) {
                events.add(new Event(1, meltDay, pile));
            }
        }

        Collections.sort(events);

        int j = 0;
        int piles = 0;

        for (int i = 0; i < n; i++) {
            long sumDay = 0;

            while (j < events.size() && events.get(j).day == i && events.get(j).type == 0) {
                j++;
                piles++;
            }

            while (j < events.size() && events.get(j).day == i && events.get(j).type == 1) {
                Pile pile = events.get(j).pile;
                sumDay += ((pile.day == 0) ? 0L : acct[pile.day - 1]) + pile.size - ((i == 0) ? 0L : acct[i - 1]);
                j++;
                piles--;
            }

            sumDay += 1L * piles * t[i];
            out.print(sumDay + ((i < n - 1) ? " " : ""));
        }

        out.println();
    }

    class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() throws Exception {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws Exception {
            while ((st == null) || (!st.hasMoreTokens())) {
                String t = br.readLine();
                if (t == null) {
                    return null;
                }
                st = new StringTokenizer(t);
            }
            return st.nextToken();
        }

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

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

        boolean nextBoolean() throws Exception {
            return Boolean.parseBoolean(next());
        }

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