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.InputStream;
import java.io.InputStreamReader;
import java.util.*;



public class A {
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int N = Reader.nextInt();
        long[] vol = new long[N];
        long[] temp = new long[N];
        long[] piles = new long[N+1];
        long[] sum = new long[N+1];
        long[] left = new long[N+1];
        long[] out = new long[N+1];
        for(int i=0;i<N;i++){
            vol[i] = Reader.nextInt();
        }
        for(int i=0;i<N;i++){
            temp[i] = Reader.nextInt();
        }

        for(int i=1;i<N+1;i++){
            sum[i] = sum[i-1]+temp[i-1];
        }

        for(int i=0;i<N;i++){
            int start = i;
            int end =  N;
            while(start<end){
                int mid = (start+end)/2;
                if(sum[mid] - sum[i] < vol[i]){start = mid+1;}
                else{end = mid;}
            }
            piles[i]++;
            piles[start]--;

            if(sum[end]-sum[i]-vol[i]>0){
            left[start] += (sum[end]-sum[i]-vol[i]);}
        }
        int x = 0;
        for(int i=0;i<N;i++){
            x += piles[i];
            out[i] = x*temp[i] - left[i+1];
        }

        for(int i=0;i<N;i++){System.out.print(out[i] + " ");}

        System.out.println();


    }}
class Reader{
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */

    static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");

    }

    static String nextToken() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {

            try {







                tokenizer = new StringTokenizer(reader.readLine());







            } catch (IOException e) {







                throw new RuntimeException(e);







            }







        }







        return tokenizer.nextToken();







    }















    /** get next word */







    static String next() throws IOException {















        while ( ! tokenizer.hasMoreTokens() ) {















            //TODO add check for eof if necessary







            tokenizer = new StringTokenizer(







                    reader.readLine() );







        }







        return tokenizer.nextToken();







    }















    static int nextInt() throws IOException {















        return Integer.parseInt( next() );















    }















    static double nextDouble() throws IOException {







        return Double.parseDouble( next() );







    }















    static long nextLong() {







        return Long.parseLong(nextToken());







    }







}