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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class CF_948_C_PRODUCING_SNOW {

	static PriorityQueue<Long> ar = new PriorityQueue<>();

	static long decAllandRes(int n,long acc) {
		long res = 0;
		while( !ar.isEmpty() && ar.peek() <= n+acc)
			res+= ar.poll() - acc;
		
		res += 1L*n * (ar.size()) ;
		
		return res;

	}

	public static void main(String[] args) throws Exception {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);

		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n];
		int[] b = new int[n];

		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++)
			a[i] = Integer.parseInt(st.nextToken());

		st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++)
			b[i] = Integer.parseInt(st.nextToken());

		long acc = 0;
		for (int i = 0; i < n; i++) {
			ar.add(a[i]+acc);
			
			out.print(decAllandRes(b[i],acc) + " ");
			
			acc +=b[i];
			
		}

		out.flush();
		out.close();

	}

}

