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.*;
import java.io.*;
import java.math.*;
public class cf
{
    static int n;
    static int m;
    static Integer t[];
    static long cumt[];
    static Integer v[];
    public static int bs(int low,int high,long find)
    {
        while(low<high)
        {
            int mid=(low+high+1)/2;
            if(cumt[mid]<=find)
            low=mid;
            else
            high=mid-1;
        }
        return low;
    }
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Scanner sc=new Scanner(System.in);
        n=sc.nextInt();
        int v[]=new int[n];
        int t[]=new int[n];
        for(int i = 0 ;i<n;i++)
        v[i]=sc.nextInt();
        for(int i =0 ;i<n;i++)
        t[i]=sc.nextInt();
        long ans[]=new long[n+10];
        cumt=new long[n];
        cumt[0]=t[0];
        for(int i=1;i<n;i++)
        {
            cumt[i]=(long)cumt[i-1]+t[i];
        }
        long t1=0;
        long heaps[]=new long[n+10];
        for(int i = 0 ;i<n;i++)
        {
            long pile=v[i]+t1;
            int ind=bs(i,n-1,pile);
            while(ind<n&&pile>cumt[ind])
            ind++;
            heaps[i]++;
            t1=cumt[i];
            if(ind==n)
            continue;
            heaps[ind]--;
            if(ind==0)
            ans[ind]+=pile;
            else
            ans[ind]+=pile-cumt[ind-1];
            
        }
        int store=0;
        /*for(int i = 0 ;i<n;i++)
        {
            System.out.print(heaps[i]+" ");
        }
        System.out.println();
        for(int i = 0 ;i<n;i++)
        {
            System.out.print(ans[i]+" ");
        }*/
        for(int i = 0 ;i<n;i++)
        {
            store+=heaps[i];
            long ans1=(long)store*t[i]+ans[i];
            out.println(ans1);
        }
        out.flush();
    }
 
}