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.BufferedInputStream;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.util.PriorityQueue;
import java.util.Scanner;

public class C948 {

	public static void main(String args[]) throws Exception {
		Scanner in = new Scanner(new BufferedInputStream(System.in));
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

		int N = in.nextInt();
		int[] v = new int[N];
		int[] t = new int[N];
		for (int i = 0; i < N; i++)
			v[i] = in.nextInt();
		for (int i = 0; i < N; i++)
			t[i] = in.nextInt();

		int removed = 0;
		long prevTemp = 0;
		PriorityQueue<Long> nums = new PriorityQueue<>();
		for (int i = 0; i < N; i++) {
			nums.add(v[i] + prevTemp);

			long tot = 0;
			while (nums.size() > 0 && nums.peek() < prevTemp + t[i]) {
				removed++;
				tot += nums.poll() - prevTemp;
			}
			tot += (i - removed + 1L) * t[i];
			out.write(tot + " ");

			prevTemp += t[i];
		}

		out.flush();
	}
}
