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.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class C {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int[] vs = IntStream.range(0, n).map(x -> s.nextInt()).toArray();
        int[] ts = IntStream.range(0, n).map(x -> s.nextInt()).toArray();

        ArrayList<Long> tsAcc = new ArrayList<>();
        tsAcc.add(0L);
        for (int t : ts) tsAcc.add(t + tsAcc.get(tsAcc.size() - 1));
        tsAcc.add(Long.MAX_VALUE);

        long[] melted = new long[n];
        int[] meltedCount = new int[n];
        for (int i = 0; i < vs.length; i++) {
            long t = vs[i] + tsAcc.get(i);
            int l = 0, r = tsAcc.size() - 1;
            while (r - l > 1) {
                int c = (r+l)/2;
                if (t <= tsAcc.get(c)) r = c;
                else l = c;
            }
            if (l < n) {
                melted[l] += t - tsAcc.get(l);
                meltedCount[l]++;
            }
        }
        long[] countPerDay = new long[n];
        int count = 0;
        for (int i = 0; i < n; i++) {
            count = count + 1 - meltedCount[i];
            countPerDay[i] = count;
        }
        List<Long> results = IntStream.range(0, n).boxed().map(i -> countPerDay[i] * ts[i] + melted[i]).collect(Collectors.toList());
        System.out.println(results.stream().map(Object::toString).collect(Collectors.joining(" ")));
    }
}
