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.Arrays;
import java.util.Scanner;

public class ProducingSnow {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int days = sc.nextInt();
		sc.nextLine();
		long[] pileSizes = Arrays.stream(sc.nextLine().split(" ")).mapToLong(x -> Long.parseLong(x)).toArray();
		long[] temp = Arrays.stream(sc.nextLine().split(" ")).mapToLong(x -> Long.parseLong(x)).toArray();
		// amount of melted snow from an infinite pile from the start day to the end
		// day.
		double[] totalMelt = new double[days + 1];
		for (int i = 1; i < days + 1; i++) {
			totalMelt[i] = totalMelt[i - 1] + temp[i - 1];
		}
		// amount of extra melting each day
		long[] rem = new long[days + 1];
		// amount of change in piles fully melting each day
		long[] fullMelt = new long[days + 2];
		// amount of piles melting for the day
		long curMelt = 0;
		StringBuilder res = new StringBuilder();
		for (int i = 0; i < pileSizes.length; i++) {
			// find end melt time
			int meltTime = Arrays.binarySearch(totalMelt, pileSizes[i] + totalMelt[i] + .5);
			fullMelt[i]++;
			meltTime = -(meltTime + 1);
			if (meltTime - 1 != days) {
				long end = (pileSizes[i] + (long)(totalMelt[i])) - (long)(totalMelt[meltTime - 1]);
				fullMelt[meltTime - 1]--;
				rem[meltTime - 1] += end;
			}

			curMelt += fullMelt[i];
			long dayMelt = (temp[i] * curMelt + rem[i]);
			res.append(dayMelt + " ");
		}
		sc.close();
		System.out.println(res.substring(0, res.length() - 1));

	}
}
