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 bisect

n = int(raw_input())

V = [int(x) for x in raw_input().split()]
T = [int(x) for x in raw_input().split()]

TOTAL_T = []
s = 0
for t in T:
    s += t
    TOTAL_T.append(s)

RESTS = [None] * n
for i, v in enumerate(V):
    start = 0 if i == 0 else TOTAL_T[i - 1]
    day_of_melt = bisect.bisect_left(TOTAL_T, v + start, i)
    if day_of_melt < n:
        if not RESTS[day_of_melt]:
            RESTS[day_of_melt] = []
        RESTS[day_of_melt].append(v + start - (TOTAL_T[day_of_melt-1] if day_of_melt > 0 else 0))

already_melt = 0
answers = [0] * n
for i, x in enumerate(RESTS):
    if x:
        already_melt += len(x)
        answers[i] += sum(x)
    answers[i] += (i + 1 - already_melt) * T[i]
print ' '.join([str(x) for x in answers])