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.*;
 
public class Main{
    
    
   public static void main(String[] args) {
      // Use the Scanner class
      Scanner sc = new Scanner(System.in);  
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String
      */
      
      int N = sc.nextInt();
      
      long[] v = new long[N];
      long[] t = new long[N];
      
      for(int i=0; i<N; i++){
          v[i]=sc.nextLong();
      }
      
      for(int i=0; i<N; i++){
          t[i]=sc.nextLong();
      }
      
      long sum=0;
      PriorityQueue<Long> pq = new PriorityQueue<>();
      
      for(int i=0; i<N; i++){
          pq.add(v[i]+sum);
          sum+=t[i];
          
         long melt=0;
         while(!pq.isEmpty() && pq.peek()<=sum){
             melt+=pq.poll()-(sum-t[i]);
         }
         
         melt+=pq.size()*t[i];
         System.out.print(melt+(i==N-1?"\n":" "));
      }
      
   }
    
}