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 Main {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws IOException {
        MultiSet<Long> set = new MultiSet<>();
        int n = Integer.parseInt(br.readLine());
        String[] days = br.readLine().split(" ");
        String[] temp = br.readLine().split(" ");
        StringBuilder sol = new StringBuilder();

        long tmpSum = 0;
        for(int i = 0; i < n; ++i) {
            long currSum = 0;
            long currDay = Long.parseLong(days[i]);
            long currTemp = Long.parseLong(temp[i]);
            set.add(currDay + tmpSum);

            while(set.size != 0 && set.firstKey() <= tmpSum + currTemp) {
                currSum += set.firstKey() - tmpSum;
                set.delete(set.firstKey());
            }

            currSum += (long) set.size * currTemp;
            tmpSum += currTemp;

            sol.append(currSum + " ");
        }

        sol.setLength(sol.length() - 1);
        System.out.println(sol.toString());

    }

    static class MultiSet<T> extends TreeMap<T, Integer> {
        int size = 0;

        public void add(T key) {
            Integer q = super.get(key);
            super.put(key, q == null ? 1 : q + 1);
            size++;
        }

        public void delete(T key) {
            Integer q = super.get(key);
            if(q == null) throw new NullPointerException("Key not in MultiSet");

            if(q == 1) super.remove(key);
            else super.put(key, q - 1);
            size--;
        }
    }
}

