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.*;

public class TaskC {
	FastScanner in;
	PrintWriter out;

	public void solve() throws IOException {
		int n = in.nextInt();
		long[] v = new long[n];
		long[] t = new long[n];
		for (int i = 0; i < n; i++) {
			v[i] = in.nextInt();
		}
		for (int i = 0; i < n; i++) {
			t[i] = in.nextInt();
		}
		long[] h = new long[n + 1];
		int l = 0;
		long k = 0;
		for (int i = 0; i < n; i++) {
			l++;
			h[l] = v[i] + k;
			int ll = l;
			while ((ll / 2 > 0) && (h[ll / 2] > h[ll])) {
				long tmp = h[ll];
				h[ll] = h[ll / 2];
				h[ll / 2] = tmp;
				ll /= 2;
			}
			long x = 0;
			while ((l > 0) && (h[1] <= k + t[i])) {
				x += h[1] - k;
				h[1] = h[l];
				l--;
				int p = 1;
				while (p * 2 <= l) {
					if (p * 2 == l) {
						if (h[p] > h[p * 2]) {
							long tmp = h[p];
							h[p] = h[p * 2];
							h[p * 2] = tmp;
							p *= 2;
						} else {
							break;
						}
					} else {
						if (h[p * 2] > h[p * 2 + 1]) {
							if (h[p] > h[p * 2 + 1]) {
								long tmp = h[p];
								h[p] = h[p * 2 + 1];
								h[p * 2 + 1] = tmp;
								p = p * 2 + 1;
							} else {
								break;
							}
						} else {
							if (h[p] > h[p * 2]) {
								long tmp = h[p];
								h[p] = h[p * 2];
								h[p * 2] = tmp;
								p *= 2;
							} else {
								break;
							}
						}
					}
				}
			}
			out.print((x + l * t[i]) + " ");
			k += t[i];
		}
	}

	public void run() {
		try {
			in = new FastScanner(new InputStreamReader(System.in));
			out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
					System.out)));
			solve();
			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(InputStreamReader isr) {
			br = new BufferedReader(isr);

		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

	public static void main(String[] arg) {
		new TaskC().run();
	}
}