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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Code {
    public static void main(String[] args) {
        // Use the Scanner class
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        int n = sc.nextInt();

        long[] V = new long[n];
        long[] T = new long[n];

        for (int i = 0; i < n; ++i) {
            V[i] = sc.nextInt();
        }

        for (int i = 0; i < n; ++i) {
            T[i] = sc.nextInt();
        }

        Item[] hills = new Item[n];
        for (int i = 0; i < n; ++i) {
            hills[i] = new Item(i+1, V[i]);
        }

        long[] ps = new long[1+n];
        ps[0] = 0;
        for (int i = 0; i < n; ++i) {
            ps[i+1] = ps[i] + T[i];
        }

        ItemComparator comp = new ItemComparator(ps);
        PriorityQueue<Item> q = new PriorityQueue<>(comp);
        long[] ans = new long[n];

        for (int i = 1; i <= n; ++i) {
            comp.time = i;
            q.add(hills[i-1]);
            long total_melt = 0;
            total_melt += T[i-1]*q.size();
            while (!q.isEmpty() && q.peek().get_current_val(i, ps) <= 0) {
                Item cur = q.poll();
                long cur_val = cur.get_current_val(i, ps);
                total_melt += cur_val;
            }
            ans[i-1] = total_melt;
        }

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; ++i) {
            sb.append(ans[i] + " ");
        }
        System.out.println(sb.toString());
    }

    static class ItemComparator implements Comparator<Item> {

        long[] ps;
        int time;

        public ItemComparator(long[] ps) {
            this.ps = ps;
            time = 1;
        }

        @Override
        public int compare(Item o1, Item o2) {
            return Long.compare(o1.get_current_val(time, ps), o2.get_current_val(time, ps));
        }
    }

    static class Item {
        int idx;
        long initial_value;

        public Item(int idx, long init_val) {
            this.idx = idx;
            this.initial_value = init_val;
        }

        public long get_current_val(int time, long[] ps) {

            return initial_value - (ps[time] - ps[idx-1]);
        }
    }


    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
       BufferedReader br;
       StringTokenizer st;

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

       String next() {
           while (st == null || !st.hasMoreElements()) {
               try {
                   st = new StringTokenizer(br.readLine());
               } catch (IOException e) {
                   e.printStackTrace();
               }
           }
           return st.nextToken();
       }

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

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

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

       String nextLine(){
           String str = "";
       try {
          str = br.readLine();
       } catch (IOException e) {
          e.printStackTrace();
       }
       return str;
       }

    }
}