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.
from sys import stdin


def binary_search(l, r, val):
    global prefix
    i, j = l, r
    while i < j:
        mid = (i + j) // 2
        ptr = prefix[mid]
        if ptr <= val:
            i = mid + 1
        else:
            j = mid
    return i

n = int(stdin.buffer.readline())
V = list(map(int, stdin.buffer.readline().split()))
T = list(map(int, stdin.buffer.readline().split()))

cnt = [0] * (n + 1)
res = [0] * (n + 1)
prefix = [0] * (n + 1)

for i in range(n):
    if i == 0:
        prefix[i] = T[i]
    else:
        prefix[i] = prefix[i - 1] + T[i]

for i in range(n):
    id = None
    if i == 0:
        id = binary_search(i, n - 1, V[i])
    else:
        id = binary_search(i, n - 1, V[i] + prefix[i - 1])
    if id == n - 1 and V[i] + prefix[i - 1] > prefix[id]:
        id += 1
    cnt[i] += 1
    cnt[id] -= 1
    if id == n:
        continue
    if i == 0:
        res[id] += (T[id] - prefix[id] + V[i])
    else:
        res[id] += (T[id] - prefix[id] + V[i] + prefix[i - 1])

for i in range(n):
    if i > 0:
        cnt[i] += cnt[i - 1]
    res[i] += cnt[i] * T[i]

for i in range(n):
    if i == n - 1:
        print(res[i])
    else:
        print(res[i], end = ' ')