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.io.*;
import java.util.*;

public class R470_C {
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");

	public static void main(String[] args) throws Exception {
      int n = readInt();
      int[] v = new int[n];
      int[] t = new int[n];
      for(int i = 0; i < n; ++i)
         v[i] = readInt();
      for(int i = 0; i < n; ++i)
         t[i] = readInt();
      
      long s = 0;
      PriorityQueue<Long> q = new PriorityQueue();
      for(int i = 0; i < n; ++i) {
         long sum = 0;
         q.add(s+v[i]);
         
         while(!q.isEmpty() && q.peek() <= s+t[i])
            sum += q.poll()-s;
         sum += (long)t[i]*q.size();
         
         s += t[i];
         System.out.print(sum+" ");
      }
      
      System.out.println();
   }

	static String readString() throws Exception {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(stdin.readLine());
		return st.nextToken();
	}
	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	static long readLong() throws Exception {
		return Long.parseLong(readString());
	}
	static double readDouble() throws Exception {
		return Double.parseDouble(readString());
	}
}
