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.math.*;

public class test {
	public static void main(String[] args) throws IOException {
		Scanner s = new Scanner(System.in);
		int N = Integer.parseInt(s.nextLine());
		long[] v = new long[N];
		long[] t = new long[N];
		StringTokenizer st = new StringTokenizer(s.nextLine());
		for (int i = 0; i < N; i++) {
			v[i] = Long.parseLong(st.nextToken());
		}
		StringTokenizer ts = new StringTokenizer(s.nextLine());
		for (int i = 0; i < N; i++) {
			t[i] = Long.parseLong(ts.nextToken());
		}
		long[] totalMelt = new long[N];
		totalMelt[0] = t[0];
		for (int i = 1; i < N; i++) {
			totalMelt[i] = totalMelt[i - 1] + t[i];
		}
		long[] ret = new long[N];
		int[] incrementor = new int[N];
		for (int i = 0; i < N; i++) {
			int left = i;
			int right = N - 1;
			int middle = (left + right) / 2;
			while (left < right) {
				if (left + 1 == right) {
					long cringe = 0;
					if (i > 0) {
						cringe = totalMelt[right] - totalMelt[i - 1];
					} else {
						cringe = totalMelt[right];
					}
					left = right;
					if (cringe <= v[i]) {
						middle = right;
					} else {
						middle = left;
					}
				} else {
					middle = (left + right) / 2;
					long cumulative;
					if (i > 0) {
						cumulative = totalMelt[middle] - totalMelt[i - 1];
					} else {
						cumulative = totalMelt[middle];
					}
					if (cumulative < v[i]) {
						left = middle;
					} else if (cumulative == v[i]) {
						left = middle;
						right = middle;
					} else { // if cumulative > v[i]
						right = middle - 1;
					}
				}
			}
			long cring = 0;
			if (i > 0) {
				cring = totalMelt[middle] - totalMelt[i - 1];
			} else {
				cring = totalMelt[middle];
			}
			while (cring > v[i]) {
				cring -= t[middle];
				middle--;
			}
			if (middle + 1 < N) {
				ret[middle + 1] += v[i] - cring;
			}
			if (middle >= i) {
				incrementor[i]++;
				if (middle + 1 < N) {
					incrementor[middle + 1]--;
				}
			}
		}
		int curr = 0;
		for (int i = 0; i < N; i++) {
			curr += incrementor[i];
			ret[i] += curr * t[i];
		}
		for (int i = 0; i < N; i++) {
			System.out.print(ret[i] + " ");
		}
		s.close();
	}
}