Codeforces-470 div2 C题

C. 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 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

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.

题目大意：就是求每天会融化多少雪。

思路：这题目两种思路

1、二分查找第i堆雪什么时候融化。

2、优先队列+前缀和 （优先队列也可以用multiset ）

开始我只想到是优先队列，但是怎么处理那些剩下的雪没有好的方法。

后面又想到了是前缀和，但是又没和优先队列联系起来。

AC代码

#include<iostream>
#include<bits/stdc++.h>
#define ll long long
using namespace std;
priority_queue < ll , vector < ll > , greater < ll > > q;
ll a[100500];
ll c[100500];
ll sum[100500];
int main(){
    ll n;
    cin>>n;
    for(ll i=1;i<=n;i++)
        scanf("%d",a+i);
    for(ll i=1;i<=n;i++){
        scanf("%d",c+i);
        sum[i]=c[i]+sum[i-1];
    }
    for(ll i=1;i<=n;i++){
        q.push(a[i]+sum[i-1]);   //关键一步！！！让新加的雪堆变成第一天就已经放置的雪堆！！！
        ll ans=0;
        while(!q.empty()&&q.top()<sum[i]){
            ans+=(q.top()-sum[i-1]);
            q.pop();
        }
        ans+=c[i]*q.size();
        cout<<ans<<' ';
    }
    cout<<endl;
    return 0;
}