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.
// package cf948;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.Collectors;

public class CFC {
    private static final String INPUT = "5\n" +
            "30 25 20 15 10\n" +
            "9 10 12 4 13\n";

    FastScanner sc;

    public static void main(String[] args) {
        new CFC().run();
    }

    public void run() {
        sc = new FastScanner(oj ? System.in : new ByteArrayInputStream(INPUT.getBytes()));

        long s = System.currentTimeMillis();
        solve();
        System.out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }

    public void solve() {
        int n = sc.nextInt();
        long[] v = readLongArray(n);
        long[] t = readLongArray(n);
        long[] tplus = new long[n];
        long[] vplus = new long[n];

        long tsum = 0;
        for (int i = 0; i < n; i++) {
            tplus[i] = t[i] + tsum;
            tsum = tsum + t[i];
        }

        long vsum = 0;
        for (int i = 0; i < n; i++) {
            vplus[i] = v[i] + vsum;
            vsum = vsum + t[i];
        }

        PriorityQueue<Long> queue = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            long ans = 0;
            long cv = vplus[i];
            long ct = tplus[i];

            queue.add(cv);
            while (!queue.isEmpty() && queue.peek() <= ct) {
                ans += queue.poll() - (i==0 ? 0 : tplus[i-1]);
            }

            ans += queue.size() * t[i];
            System.out.print(ans + " ");
        }
    }

    //********************************************************************************************
    //********************************************************************************************
    //********************************************************************************************

    private static int lowerBound(int[] arr, int key) {
        int lo = 0;
        int hi = arr.length -1;
        while (lo < hi) {
            int mid = (lo + hi)/2;
            if (key <= arr[mid]) {
                hi = mid-1;
            } else {
                lo = mid+1;
            }
        }
        return arr[lo] < key ? lo + 1 : lo;
    }

    private static int upperBound(int[] arr, int key) {
        int lo = 0;
        int hi = arr.length -1;
        while (lo < hi) {
            int mid = (lo + hi)/2;
            if (key >= arr[mid]) {
                lo = mid+1;
            } else {
                hi = mid;
            }
        }
        return arr[lo] <= key ? lo + 1 : lo;
    }

    private static int ceil(double d) {
        int ret = (int) d;
        return ret == d ? ret : ret + 1;
    }

    private static int round(double d) {
        return (int) (d + 0.5);
    }

    private static int gcd(int a, int b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.intValue();
    }

    private static long gcd(long a, long b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.longValue();
    }

    private int[] readIntArray(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextInt();
        }
        return res;
    }

    private long[] readLongArray(int n) {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextLong();
        }
        return res;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

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

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }

    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}