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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        int[] vs = new int[n];
        int[] ts = new int[n];
        long[] rem = new long[n];
        int[] cnt = new int[n];
        long[] T = new long[n];
        for (int i = 0; i < n; i++) {
            vs[i] = sc.nextInt();
        }
        T[0] = sc.nextInt();
        ts[0] = (int)T[0];
        for (int i = 1; i < n; i++) {
            int v = sc.nextInt();
            T[i] = v + T[i - 1];
            ts[i] = v;
        }

        for (int i = 0; i < n; i++) {
            long v = vs[i];
            if (i > 0) v += T[i - 1];
            int ind = Arrays.binarySearch(T, v);
            int r;
            if (ind >= 0) {
                while (ind > i && v == T[ind - 1]) {
                    ind--;
                }
                r = ind + 1;
            } else {
                r = -(ind + 1);
                if (r >= 0 && r < n) {
                    rem[r] += v;
                    if (r > 0) rem[r] -= T[r - 1];
                }
            }
            cnt[i]++;
            if (r < n) cnt[r]--;
        }

        int count = 0;
        StringBuilder str = new StringBuilder();
        for (int i = 0; i < n; i++) {
            count += cnt[i];
            str.append(((long)ts[i] * count + rem[i]) + " ");
        }
        System.out.println(str);
    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

        long nextLong() {
            return Long.parseLong(next());
        }

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}