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.util.*;
import java.io.*;


/**
 *
 * @author user1
 */
 
 
 
 public class Codechef {

    static class Input {
        private StringTokenizer tokenizer = null;
        private BufferedReader reader;
 
        public Input(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }
 
        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
 
        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(nextLine());
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
 
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
 
        public int[] nextIntArray(int n, int add) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt() + add;
            }
            return result;
        }
 
        public long[] nextLongArray(int n, long add) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong() + add;
            }
            return result;
        }
 
        public int[] nextIntArray(int n) {
            return nextIntArray(n, 0);
        }
 
    }

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Input s=new Input(System.in);
        int n=s.nextInt();
        long a[]=s.nextLongArray(n,0);
        long b[]=new long[n];
        long prefix[]=new long[n];
        long count[]=new long[n];
        long rem[]=new long[n];
        prefix[0]=s.nextLong();
        b[0]=prefix[0];
        for(int i=1;i<n;i++)
        {
            b[i]=s.nextLong();
            prefix[i]+=prefix[i-1]+b[i];
        }
        for(int i=0;i<n;i++)
        {
            long ab=a[i];
            if(i>0)ab+=prefix[i-1];
            
            int ind=Arrays.binarySearch(prefix,ab);
            //System.out.println(ab+" "+ind);
            int r=0;
            if(ind<0)
            {
                
             r=-(ind+1);
            if(r>=0 && r<n)
            { rem[r]+=ab;
             if(r>0)
             rem[r]-=prefix[r-1];
            }   
            }
            else{
                
                while(ind>i && ab==prefix[ind-1])
                {
                    ind--;
                }
                r=ind+1;
            }
            count[i]++;
           if(r<n)
            count[r]--;
            
            
        }
        int cnt=0;
        for(int i=0;i<n;i++)
        {
            cnt+=count[i];
            System.out.print((cnt*b[i]+rem[i])+" ");
        }
        
}
}