human
Write me a Python code to determine the total volume of snow melted on each day given the following:
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.
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to determine the total volume of snow melted on each day.

# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
mod=10**9+7
# sys.setrecursionlimit(10**6)
from bisect import bisect

def main():
    n=int(input())
    v=list(map(int,input().split()))
    t=list(map(int,input().split()))
    z=0
    temp=[0]
    for item in t:
        z+=item
        temp.append(z)
    # print(temp)
    d=dict()
    dff=dict()
    for i,item in enumerate(v):
        z=bisect(temp,item+temp[i])
        z-=1
        if z not in d:
            d[z]=[]
            dff[z]=[]
        d[z].append(item)
        dff[z].append(item-(temp[z]-temp[i]))
    # print(d)
    # print(dff)
    z=0
    ans=[]
    for i in range(n):
        x=0
        if i in d:
            z+=(1-len(d[i]))
            for item in dff[i]:
                x+=(item)
        else:
            z+=1
        x+=(z*t[i])
        ans.append(x)
    print(*ans)

#----------------------------------------------------------------------------------------
def nouse0():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse1():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse2():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')



# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b),...