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.
# -*- coding: utf - 8 -*-
"""""""""""""""""""""""""""""""""""""""""""""
|    author: mr.math - Hakimov Rahimjon     |
|    e-mail: mr.math0777@gmail.com          |
|    created: 10.03.2018 22:24              |
"""""""""""""""""""""""""""""""""""""""""""""
# inp = open("input.txt", "r"); input = inp.readline; out = open("output.txt", "w"); print = out.write
TN = 1
from itertools import accumulate
import bisect


# ===========================================


def solution():
    n = int(input())
    v = list(map(int, input().split()))
    t = list(map(int, input().split()))
    ns = [0] * n
    lo = [0] * n
    tt = list(accumulate(t))
    for i in range(n):
        dd = v[i]
        a = 0
        if i != 0:
            dd += tt[i - 1]
            a = tt[i - 1]
        ns[i] += 1
        k = bisect.bisect_right(tt, dd)
        if k < n:
            ns[k] -= 1

            lo[k] += v[i] + a
            if k != 0:
                lo[k] -= tt[k - 1]
    ns = list(accumulate(ns))
    for i in range(n):
        lo[i] += t[i] * ns[i]
    print(' '.join(list(map(str, lo))))


# ===========================================
while TN != 0:
    solution()
    TN -= 1
# ===========================================
# inp.close()
# out.close()
