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.*;
import java.util.*;

public final class Round470 {
	static Scanner sc = new Scanner(System.in);
	static long[] freq ;
	static long[] sum;
	static long[] T;
	
	public static void populate(long [] CT,long []V,int i,int start,int end){
		if(start==end && (CT[start]-CT[i]+T[i]>V[i])){
			freq[start-1]++;
			freq[i-1]--;
			sum[start]+=V[i]-(CT[start-1]-CT[i-1]);
			return;
		}
		else if(start==end){
			freq[i-1]--;
			freq[start]++;
			return;
		}
		int mid = (start+end)/2;
		if(CT[mid]-CT[i]+T[i]>V[i]){
			populate(CT,V,i,start,mid);
		}
		else{
			populate(CT,V,i,mid+1,end);
		}
	}
	public static void main(String args[]) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = sc.nextInt();
		freq = new long[N+2];
		long V[] = new long[N+2];
		T = new long[N+2];
		sum = new long[N+2];
		long CT[] = new long[N+2];
		for(int i=1;i<N+1;i++)
			V[i]=sc.nextLong();
		
		for(int i=1;i<N+1;i++)
			T[i]=sc.nextLong();
		
		CT[0]=T[0];
		for(int i=1;i<N+1;i++)
			CT[i]= CT[i-1]+T[i];
		
		for(int i=1;i<N+1;i++){
			populate(CT,V,i,i,N);
			//System.out.println(Arrays.toString(freq)+"   "+Arrays.toString(sum));
		}
		long ans[] = new long[N+2];
		long tf[] = new long[N+2];
		for(int i=N;i>=1;i--){
			tf[i]=tf[i+1]+freq[i];
		}
		for(int i=N;i>=1;i--)
		{
			ans[i]=tf[i]*T[i]+sum[i];
		}
		for(int i=1;i<N+1;i++)
		System.out.print(ans[i]+" ");
	}
}
