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.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {

	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int []snow=new int [n];
		for(int i=0;i<n;i++)
			snow[i]=sc.nextInt();
		long[]t=new long [n];
		long []sum=new long [n];
		for(int i=0;i<n;i++)
		{
			sum[i]=t[i]=sc.nextInt();
			if(i>0)
				sum[i]+=sum[i-1];
		}
		long []extra=new long [n];
		
		int f=0;
		int []finished=new int [n+1];
		for(int i=0;i<n;i++)
		{
			
			f+=finished[i];
			long ans=(i+1-f)*1L*t[i];
			int lo=i;
			int hi=n-1;
			int idx=-1;
			while(lo<=hi)
			{
				int mid=(lo+hi)/2;
				long s=sum[mid];
				if(i!=0)
					s-=sum[i-1];
				if(s<snow[i])
					lo=mid+1;
				else
				{
					idx=mid;
					hi=mid-1;
				}
			}
			if(idx!=-1)
			{
				long s=sum[idx];
				if(i!=0)
					s-=sum[i-1];
				extra[idx]+=s-snow[i];
				if(idx+1!=n)
				{
					finished[idx+1]++;
				}
			}
			
			
			ans-=extra[i];
			pw.print(ans+" ");
			
		}
		
		
		

		pw.close();

	}
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}
		
		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}
		
		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}
		
		public boolean ready() throws IOException {return br.ready();}


	}
}