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 sys
# from io import StringIO
#
# sys.stdin = StringIO(open(__file__.replace('.py', '.in')).read())


def bin_search_base(arr, val, base_index):
    lo = base_index
    hi = len(arr) - 1

    while lo < hi:
        if hi - lo == 1 and arr[lo] - arr[base_index] < val < arr[hi] - arr[base_index]:
            return lo

        if val >= arr[hi] - arr[base_index]:
            return hi

        c = (hi + lo) // 2
        if val < arr[c] - arr[base_index]:
            hi = c
        elif val > arr[c] - arr[base_index]:
            lo = c
        else:
            return c

    return lo


n = int(input())
volumes = list(map(int, input().split()))
temps = list(map(int, input().split()))

temp_prefix = [0]
for i in range(n):
    temp_prefix.append(temps[i] + temp_prefix[i])

gone_count = [0] * (n + 1)
remaining_count = [0] * n
gone_volume = [0] * (n + 1)

for i in range(n):
    j = bin_search_base(temp_prefix, volumes[i], i)
    gone_count[j] += 1
    gone_volume[j] += volumes[i] - (temp_prefix[j] - temp_prefix[i])

for i in range(n):
    remaining_count[i] = 1 + remaining_count[i-1] - gone_count[i]

for i in range(n):
    gone_volume[i] += remaining_count[i] * temps[i]

print(' '.join(map(str, gone_volume[:n])))
