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.*;
import java.io.*;
import java.lang.*;
import java.math.*;

public class C {
	public static void main(String[] args) throws Exception {
		//USE LONGS
		FastScanner sc = new FastScanner();
		int N = sc.nextInt();
		long[] V = new long[N];
		ArrayList<Long> T = new ArrayList<Long>();
		for(int i = 0; i < N; i++) {
			V[i] = sc.nextLong();
		}
		for(int i = 0; i < N; i++) {
			T.add(sc.nextLong());
		}
		PriorityQueue<Long> pq = new PriorityQueue<Long>();
		long[] presums = new long[N+1];
		for(int i = 1; i < presums.length; i++) {
			presums[i] = T.get(i-1) + presums[i-1];
		}
		for(int i = 0; i < N; i++) {
			V[i] = V[i] + presums[i];
		}
		for(int i = 0; i < N; i++) {
			pq.add(V[i]);
			long res = 0;
			while(!pq.isEmpty() && pq.peek() < presums[i+1]){
				res += pq.poll() - presums[i];
			}
			res += (presums[i+1]-presums[i]) * pq.size();
			System.out.print(res + " ");
		}
	}

	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

	}
}