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.*;
import java.util.*;

public class Main {
    static FastScanner in;
    static PrintWriter out;
    static final long MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        //        Scanner in = new Scanner(new File("input.txt"));
        //        Scanner in = new Scanner(System.in);
        //        System.setOut(new PrintStream(new BufferedOutputStream(new FileOutputStream("output.txt")), true));
        out = new PrintWriter(System.out);
        in = new FastScanner(System.in);
        //        in = new FastScanner("input.txt");
        int n = in.nextInt();
        long v[] = new long[n + 1];
        long t[] = new long[n + 1], f[] = new long[n + 1], m[] = new long[n + 1], ff[] = new long[n + 1],
                ans[] = new long[n + 1];
        for (int i = 1; i <= n; i++) {
            v[i] = in.nextLong();
        }
        for (int i = 1; i <= n; i++) {
            t[i] = in.nextLong();
        }
        long sumT[] = new long[n + 1];
        for (int i = 1; i <= n; i++) {
            sumT[i] = sumT[i - 1] + t[i];
        }
        for (int i = 1; i <= n; i++) {
            int l = i, r = n;
            while (l <= r) {
                int mi = (l + r) / 2;
                long sum = sumT[mi] - sumT[i - 1];
                if (v[i] >= sum) {
                    l = mi + 1;
                } else {
                    r = mi - 1;
                }
            }
            ff[i]++;
            if (l == n + 1)
                continue;
            ff[l]--;
            m[l] += v[i] - (sumT[r] - sumT[i - 1]);
        }
        for (int i = 1; i <= n; i++) {
            f[i] = f[i - 1] + ff[i];
        }
        for (int i = 1; i <= n; i++) {
            ans[i] = t[i] * f[i] + m[i];
            out.print(ans[i] + " ");
        }
        out.close();
    }
}

class Pair {
    public double first; //first member of pair
    public double second; //second member of pair

    public Pair(double first, double second) {
        this.first = first;
        this.second = second;
    }

    public Pair() {

    }

    @Override
    public boolean equals(Object o) {
        if (this == o)
            return true;
        if (!(o instanceof Pair))
            return false;
        Pair p = (Pair) o;
        return first == p.first && second == p.second;
    }

    @Override
    public int hashCode() {
        int result = (int) first;
        result = 31 * result + (int) second;
        return result;
    }
}

class PairComparable implements Comparator<Pair> {

    @Override
    public int compare(Pair o1, Pair o2) {
        if (o1.second < o2.second)
            return -1;
        else if (o1.second > o2.second)
            return 1;
        else {
            return 0;
        }
    }
}

class FastScanner {

    BufferedReader br;
    StringTokenizer tokenizer;

    FastScanner(String fileName) throws FileNotFoundException {
        this(new FileInputStream(new File(fileName)));
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
    }

    String nextLine() throws IOException {
        tokenizer = null;
        return br.readLine();
    }

    String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

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

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

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

    char nextChar() throws IOException {
        return next().charAt(0);
    }
}