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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;

// http://codeforces.com/contest/948/problem/C soln
public class Main2 {

	public Main2() throws Exception {

		BufferedWriter out;
		try {
			BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
			out = new BufferedWriter(new OutputStreamWriter(System.out));

			int n = Integer.parseInt(in.readLine());

			// while (t-- > 0) {
			// int n = Integer.parseInt(in.readLine());
			String s[] = in.readLine().split(" ");

			String s1[] = in.readLine().split(" ");
			//temperature array
			long a[] = new long[s1.length];
			long sum[] = new long[s1.length];
			for (int i = 0; i < n; i++) {
				a[i] = Long.parseLong(s1[i]);
				sum[i] = (i - 1) >= 0 ? sum[i - 1] + a[i] : a[i];
			}

			ArrayList<Integer> inter = new ArrayList<>();

			// every element gives 2 intervals
			for (int i = 0; i < n; i++) {

				// first for interval on left side
//				int rindex = (i - 1) >= 0 ? i - 1 : -1;
//				int lindex = lbinarysearch(sum, 0, rindex, a[i], sum[i], a);
//				// System.out.println("lsearch:" + lindex + ":" + rindex);
//				if (lindex >= 0 && rindex >= 0) {
//					inter.add(lindex);
//					inter.add(rindex);
//				}
				// for interval on right side
				int lindex = (i) < n ? i : -1;
				int rindex = binarysearch(sum, lindex, (int) n - 1, Integer.parseInt(s[i]), sum[i], a);
//				System.out.println("rsearch:" + lindex + ":" + rindex);
				if (lindex >= 0) {
					inter.add(lindex);
					int index = rindex == -1 ? lindex : rindex;
					inter.add(index);
				}
			}
//			// 2n intervals
//			 for (Integer i : inter) {
//			 System.out.print(i + ":");
//			 }

			int ans[] = new int[s1.length];
			long extra[] = new long[n];
			int x = 0;
			// interval addition and cal extra
			int len = inter.size();
			for (int i = 0; i < len;) {
				int l = inter.get(i);
				int r = inter.get(i + 1);

				ans[l] = ans[l] + 1;
				if ((r + 1) < s1.length)
					ans[r + 1] = ans[r + 1] - 1;

				i += 2;
				
				long val = Integer.parseInt(s[x]) - (sum[r] - ((l - 1) >= 0 ?sum[l-1]:0));
				if(r+1 <n)
					extra[r+1] += val > 0 ? val : 0;
				
				x++;
			}
			
//			for(int i=0; i<n; i++){
//				System.out.println("extra:"+extra[i]);
//			}

			// System.out.println("\n");
			// for (int i = 0; i < s1.length; i++){
			// System.out.print(ans[i]+"$");
			// }
			// System.out.println("\n");
			
			for (int i = 0; i < s1.length; i++) {

				ans[i] += (i - 1) >= 0 ? ans[i - 1] : 0;
				long val = Long.parseLong(s[i]) - a[i];
				if(val >=0)
					out.write((ans[i]*a[i]+extra[i]) + " ");
				else
					out.write((ans[i]*a[i]+extra[i]+val) + " ");
				
			}

			out.write("\n");
			out.flush();
			// }
		} catch (Exception e) {
			// TODO Auto-generated catch block
			System.out.println(e.getMessage());
			e.printStackTrace();
		}

	}

	private int binarysearch(long[] sum, int i, int rindex, long key, long base, long[] a) {

		int low = i;
		int high = rindex;

		while (low >= 0 && low < high) {

			int mid = low + (high - low + 1) / 2;

			if (sum[mid] - ((i - 1) >= 0 ?sum[i-1]:0) > key)
				high = mid - 1;
			else
				low = mid;
		}

//		if (low >= 0 && sum[low] - base - a[low] > key)
//			return -1;

		return low;
	}

	private int lbinarysearch(long[] sum, int i, int rindex, long key, long base, long[] a) {

		int low = i;
		int high = rindex;

		while (low < high) {

			int mid = low + (high - low) / 2;

			if (base - sum[mid] - key > key)
				low = mid + 1;
			else
				high = mid;
		}

		if (base - sum[low] - key > key)
			return -1;

		return low;
	}

	public static void main(String[] args) throws Exception {
		new Main2();
	}
}
