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 P950A {
  public static void main(String[] args) throws Throwable {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] v = new int[n];
    int[] t = new int[n];
    long[] frac = new long[n];
    long[] cum = new long[n];
    for (int i = 0; i < n; i++)
      v[i] = sc.nextInt();
    for (int i = 0; i < n; i++)
      t[i] = sc.nextInt();
    cum[0] = t[0];
    for (int i = 1; i < n; i++)
      cum[i] = cum[i - 1] + t[i];
    int[] away = new int[n];
    for (int i = 0; i < n; i++) {
      int cur = v[i];
      int lo = i, hi = n - 1, ans = n;
      while (lo <= hi) {
        int mid = ((lo + hi) >> 1);
        long sum = cum[mid];
        if (i > 0)
          sum -= cum[i - 1];
        if (sum > cur) {
          ans = mid;
          hi = mid - 1;
        } else {
          lo = mid + 1;
        }
      }
      if (ans < n) {
        away[ans]--;
        int cumm = 0;
        if (ans > 0)
          cumm += cum[ans - 1];
        if (i > 0)
          cumm -= cum[i - 1];
        int rem = cur - cumm;
        frac[ans] += rem;
      }
    }
    PrintWriter pw = new PrintWriter(System.out);
    long cnt = 0;
    for (int i = 0; i < n; i++) {
      cnt++;
      cnt += away[i];
      pw.print(t[i] * 1l * cnt + frac[i] + " ");
    }
    pw.println();
    pw.flush();
  }

  static class Scanner {
    StringTokenizer st;
    BufferedReader br;

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

    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 double nextDouble() throws IOException {
      return Double.parseDouble(next());
    }

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