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.*;



public class Main {
   
    static long times[];
    static long add[];
    
    
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner(System.in);
        int n=sc.nextInt();
        long snow[]=new long[n];
        long melt[]=new long[n];
        long psum[]=new long[n];
        times=new long[n+3];
        add=new long[n+3];
        
        for(int i=0;i<n;i++){
            snow[i]=sc.nextInt();
        }
        for(int i=0;i<n;i++){
            melt[i]=sc.nextInt();
            psum[i]=melt[i];
        }
        for(int i=1;i<n;i++){
            psum[i]+=psum[i-1];
        }
        for(int i=0;i<n;i++){
            if(i==0){
                bs(snow[i],i,psum,0);
            }else{
                bs(snow[i],i,psum,psum[i-1]);
            }
        }
       
        long []ans=new long[n];
        int sum=0;
       for(int i=0;i<n;i++){
           sum+=times[i];
           ans[i]=sum*melt[i];
           ans[i]-=add[i];
       }
       StringBuilder out=new StringBuilder();
      for(int i=0;i<n;i++){
          out.append(ans[i]+" ");
      }
        System.out.println(out.toString());
        
        
        
    }
    public static void bs(long snow,int s,long ps[],long del){
        int idx=s;
        int n=ps.length-1;
        int e=ps.length-1;
        int ans=-1;
        while(s<=e){
            int m=(s+e)/2;
            if(snow>=ps[m]-del){
                ans=m;
                s=m+1;
            }else{
                e=m-1;
            }
        }
        if(ans!=-1){
            times[idx]++;
            times[ans+2]--;
            if(ans<n)
            add[ans+1]+=(ps[ans+1]-del)-snow;
        }else{
            times[idx]++;
            times[idx+1]--;
            add[idx]+=(ps[idx]-del)-snow;
        }
        
    }
    
    
    
    static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
            public FastScanner(InputStream i) {
	        br =  new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
	    public String next() throws IOException {
	        if(st.hasMoreTokens())return st.nextToken();
                else st = new StringTokenizer(br.readLine());
	        return next();
	    }
	    public int nextInt() throws IOException {return Integer.parseInt(next());}
	    public long nextLong() throws IOException {return Long.parseLong(next());}
	    public double nextDouble() throws IOException {return Double.parseDouble(next());}
	}
}