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.LinkedList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		
		int N = input.nextInt();
		
		long[] arr = new long[N];
		long[] temp = new long[N];
		long[] cumul = new long[N];
		
		for (int i = 0; i < N; i++)
			arr[i] = input.nextInt();
		for (int i = 0; i < N; i++)
			temp[i] = input.nextInt();
		cumul[0] = temp[0];
		for (int i = 1; i < N; i++)
			cumul[i] = cumul[i - 1] + temp[i];
		
		LinkedList<Integer>[] ls = new LinkedList[N];
		for (int i = 0; i < N; i++)
			ls[i] = new LinkedList<Integer>();
		
		for (int i = 0; i < N; i++) {
			int lo = 0;
			int hi = N - 1;
			long last = i == 0 ? 0 : cumul[i - 1];
			
			while (lo <= hi) {
				int mid = (lo + hi) / 2;
				if (cumul[mid] < arr[i] + last)
					lo = mid + 1;
				else
					hi = mid - 1;
			}
			
			if (lo < N)
				ls[lo].add(i);
		}
		
		int num = 0;
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < N; i++) {
			long sum = ++num * temp[i];
			for (int x : ls[i]) {
				sum += arr[x] - cumul[i] + (x == 0 ? 0 : cumul[x - 1]);
				num--;
			}
			sb.append(sum);
			if (i != N - 1)
				sb.append(" ");
			else
				sb.append("\n");
		}
		
		System.out.println(sb.toString());
		
	}
}
