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.


import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        long[] v=new long[n+1];  //雪堆的初始大小
        long[] t=new long[n+1];  //每天的温度
        long[] pre=new long[n+1];  //温度的前缀和
        for (int i = 1; i <=n ; i++) {
            v[i]=sc.nextLong();
        }
        for (int i = 1; i <=n ; i++) {
            t[i]=sc.nextLong();
            pre[i]=pre[i-1]+t[i];
        }
        Queue<Long> q=new PriorityQueue<Long>();
        for (int i = 1; i <=n ; i++) {
            long ans=0;
            q.add(v[i]+pre[i-1]);
            ans+=t[i]*q.size();//队列里都是可以消的
            while (!q.isEmpty()&&q.peek()<=pre[i]){
                ans+=(q.peek()-pre[i]);
                q.poll();
            }

            System.out.print(ans+" ");
        }

    }
}
