思维训练-Producing Snow

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 V_iand 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 T_i, each pile will reduce its volume by T_i. 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, ..., V_N(0 ≤ V_i ≤ 10⁹), where V_i is the initial size of a snow pile made on the day i.

The third line contains N integers T₁, T₂, ..., T_N(0 ≤ T_i ≤ 10⁹), where T_i 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.

Time limit1000 msMemory limit

262144 kB

#include <iostream>

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
using namespace std;
typedef long long LL;

struct node
{
    LL v,t;
}snow[10005];
int n;

int main()
{
    scanf("%d",&n);
    for(int i=0;i<n;i++)    scanf("%lld",&snow[i].v);
    for(int i=0;i<n;i++)    scanf("%lld",&snow[i].t);
    LL num[10005];
    memset(num,0,sizeof(num));
    for(int day=0;day<n;day++)
    {
        for(int i=0;i<=day;i++)
        {
            if(snow[i].v==0) continue;
            if(snow[i].v<=snow[day].t){
                num[day]+=snow[i].v;
                snow[i].v=0;
            }
            else{
                num[day]+=snow[day].t;
                snow[i].v-=snow[day].t;
            }
        }
    }
    for(int i=0;i<n-1;i++)
    {
        printf("%lld ",num[i]);
    }
    printf("%lld\n",num[n-1]);

    return 0;
}