codeforces 923B producing snow

B. Producing Snow

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 Viand 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

Copy

3
10 10 5
5 7 2

output

5 12 4

input

Copy

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.

首先开sum数组记录每天温度消耗雪量的前缀和，然后使用升序的优先队列，队列中存放的是当天那堆雪与前一天的前缀和的和。用这个值与当天前缀和比较，即可知当天的每堆雪有没有融化完。如果融化完，我们就把他算入当天融化量并清出队列。

#include <iostream>
#include<queue>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=1e5+5;
int v[maxn];
long long t[maxn];
long long sum[maxn];
int n;
priority_queue<long long ,vector<long long >,greater<long long > >q;
int main()
{
      while(cin>>n)
    {
        memset(t,0,sizeof(t));
        memset(sum,0,sizeof(sum));
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&v[i]);
        }
         for(int i=1;i<=n;i++)
        {
            scanf("%d",&t[i]);
            sum[i]=sum[i-1]+t[i];
        }
        for(int i=1;i<=n;i++)
        {
            long long ans=0;
            q.push(v[i]+sum[i-1]);
            // cout<<"dkvm";
            while(!q.empty()&&q.top()<=sum[i])
            {
                ans+=q.top()-sum[i-1];
                q.pop();
            }

            ans+=q.size()*t[i];
            cout<<ans<<" ";
        }
        cout<<endl;
    }
    return 0;
}