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 math import *
from collections import *

def bs(x,i):
    l = i
    r = n-1
    if(i != 0):
        while(l <= r):
            mid = (l+r)//2
            if(mid == n-1):
                return mid
            if(pre[mid]-pre[i-1] > x and pre[mid-1]-pre[i-1] < x):
                return mid
            if(pre[mid]-pre[i-1] == x):
                return mid
            if(pre[mid]-pre[i-1] > x):
                r = mid - 1
            else:
                l = mid + 1
    else:
        while(l <= r):
            mid = (l+r)//2
            if(mid == n-1):
                return mid
            if(pre[mid] > x and pre[mid-1] < x):
                return mid
            if(pre[mid] == x):
                return mid
            if(pre[mid] > x):
                r = mid - 1
            else:
                l = mid + 1
    return mid

n = int(input())
l = list(map(int,input().split()))
t = list(map(int,input().split()))
pre = [t[0]]
for i in range(1,n):
    pre.append(pre[i-1] + t[i])
dis = [0 for i in range(n)]
val = [0 for i in range(n)]
for i in range(n):
    dis[i] = bs(l[i],i)
    #print(dis[i])
    if dis[i] > 0:
        if i > 0:
            if(l[i] > pre[dis[i]] - pre[i-1]):
                #print(i)
                val[dis[i]] += t[dis[i]]
            else:
                val[dis[i]] += l[i] - pre[dis[i]-1] + pre[i-1]
        else:
            if(l[i] > pre[dis[i]]):
                val[dis[i]] += t[dis[i]]
            else:
                val[dis[i]] += l[i] - pre[dis[i]-1]
    else:
        if(l[i] > pre[dis[i]]):
            val[dis[i]] += t[dis[i]]
        else:
            val[dis[i]] += l[0]
ans = [0 for i in range(n)]
for i in range(n):
    ans[i] += 1
    ans[dis[i]] -= 1
for i in range(1,n):
    ans[i] += ans[i-1]
for i in range(n):
    ans[i] *= t[i]
    ans[i] += val[i]
'''
print(pre)
print(dis)
print(val)
'''
for i in ans:
    print(i,end = " ")
print()

