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.text.*;
import java.util.*;
import java.math.*;
public class C {
	public static void main(String[] args) throws Exception {
		new C().run();
	}
	public void run() throws Exception {
		FastScanner f = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = f.nextInt();
		long[] add = new long[n];
		long[] bounds = new long[n+1];
		for(int i = 0; i < n; i++)
			add[i] = f.nextLong();
		for(int i = 0; i < n; i++)
			bounds[i+1] = f.nextLong() + bounds[i];
		for(int i = 0; i < n; i++) 
			add[i] += bounds[i];
		PriorityQueue<Long> pq = new PriorityQueue<Long>();
		for(int i = 0; i < n; i++) {
			pq.add(add[i]);
			long cnt = 0;
			while(!pq.isEmpty() && pq.peek() < bounds[i+1]) {
				cnt += pq.poll()-bounds[i];
			}
			cnt += (bounds[i+1] - bounds[i])*pq.size();
			out.print(cnt);
			out.print(" ");
		}
		out.flush();
	}
	int[] BIT;
	public void add(int n, int i) {
		i++;
		while(i < BIT.length) {
			BIT[i] += n;
			i += i & -i;
		}
	}
	public int query(int i) {
		i++;
		int res = 0;
		while(i > 0) {
			res += BIT[i];
			i -= i & -i;
		}
		return 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);
        	}
        }


    }
}
