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.
// package CF;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int [] v = new int[n];
		long [] t = new long[n];
		long [] num = new long[n];
		long [] mod = new long[n];
		for (int i = 0; i < v.length; i++) {
			v[i] = sc.nextInt();
		}
		for (int i = 0; i < v.length; i++) {
			t[i] = sc.nextInt();
			if(i > 0)
				t[i] += t[i-1];
		}
		for (int i = 0; i < num.length; i++) {
			long tmp = v[i]+(i-1<0?0:t[i-1]);
			int lo = i, hi = n-1, ans = -1;
			while(lo <= hi){
				int mid = (lo + hi)/2;
				if(t[mid] >= tmp){
					ans = mid;
					hi = mid-1;
				}
				else{
					lo = mid+1;
				}
			}
			num[i]++;
//			System.out.println(ans);
			if(ans != -1)
			{
				if(t[ans] == tmp)
					ans++;
				else{
					mod[ans] += Math.max(0, tmp-(ans == 0?0:t[ans-1]));
				}
				if(ans < n)
					num[ans]--;
			}
		}
		for (int i = 1; i < num.length; i++) {
			num[i] += num[i-1];
		}
		for (int i = 0; i < num.length; i++) {
			out.print(num[i]*(t[i]-(i-1<0?0:t[i-1]))+mod[i] + " ");
		}
		out.flush();
		out.close();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader fileReader) {
			br = new BufferedReader(fileReader);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}