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.

/**
 * Date: 09 Mar, 2018
 * Link :
 *
 * @author Prasad-Chaudhari
 * @email prasadc8897@gmail.com
 */

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

public class New_File_5 {

    public static void main (String[] args) throws java.lang.Exception {
        FastIO2 in = new FastIO2();
        int n = in.ni();
        int v[] = in.gia(n);
        int t[] = in.gia(n);
        long sum[] = new long[n];
        sum[0] = t[0];
        for(int i=1;i<n;i++){
            sum[i] = sum[i-1]+t[i];
        }
        LazyProp lp = new LazyProp(n);
        long sum2[] = new long[n];
        if(v[0]<t[0]){
            sum2[0] = v[0];
        }
        else{
            int index = Arrays.binarySearch(sum,0,n,v[0]);
            if(index<0){
                index = 0-(index+1);
            }
            if(index<0){
                sum2[0]+=v[0];
            }
            else if(index==n){
                lp.insert(0,n-1,0,0,n-1,1);
            }
            else{
                lp.insert(0,n-1,0,0,index,1);
                sum2[index] = v[0]-sum[index];
            }
        }
        for(int i=1;i<n;i++){
            int index = Arrays.binarySearch(sum,i,n,v[i]+sum[i-1]);
            if(index<0){
                index = -(index+1);
            }
            if(index<i){
                sum2[i]+=v[i];
            }
            else if(index==n){
                lp.insert(0,n-1,0,i,n-1,1);
            }
            else{
                lp.insert(0,n-1,0,i,index,1);
                sum2[index] += v[i]-(sum[index]-sum[i-1]);
            }
        }
        for(int i=0;i<n;i++){
            long t2 = t[i];
            long p=lp.get(0,n-1,0,i);
            t2 = t2*p+sum2[i];
            System.out.print(t2+" ");
        }
    }

    static class FastIO2 {

        private final BufferedReader br;
        private String s[];
        private int index;

        public FastIO2() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            return br.readLine();
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if(s == null){
                s = br.readLine().split(" ");
            }
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }
}

class LazyProp {

    int n;
    long tree[];

    public LazyProp(int si) {
        double x = Math.log(si) / Math.log(2);
        n = (int)(Math.pow(2, Math.ceil(x) + 1)) + 1;
        tree = new long[n];
    }

    public void insert(int s, int e, int pos, int l, int r, long d) {
        if (l <= s && e <= r) {
            tree[pos] += d;
            return;
        }
        if (r < s || l > e) {
            return;
        }
        int mid = (s + e) / 2;
        insert(s, mid, 2 * pos + 1, l, r, d);
        insert(mid + 1, e, 2 * pos + 2, l, r, d);
    }

    public long get(int s, int e, int pos, int index) {
        if (s == e) {
            return tree[pos];
        }
        if (2 * pos + 1 < n) {
            tree[2 * pos + 1] += tree[pos];
        }
        if (2 * pos + 2 < n) {
            tree[2 * pos + 2] += tree[pos];
        }
        tree[pos] = 0;
        int mid = (s + e) / 2;
        if (index <= mid) {
            return get(s, mid, 2 * pos + 1, index);
        } else {
            return get(mid + 1, e, 2 * pos + 2, index);
        }
    }
}
