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.*;
import java.math.*;

public class C{
	
	static long v[],t[],resa[],resb[],st[]; static int n;
	static void MainMethod()throws Exception{
		n=reader.nextInt();
		v=new long[n+2]; t=new long[n+2];resa=new long[n+2];resb=new long[n+2];
		int i,j;	
		v[0]=0;
		for (i=1;i<=n;i++)v[i]=reader.nextLong();
		st=new long[n+2];
		st[0]=0;
		t[0]=0;
		for (i=1;i<=n;i++) {
			t[i]=reader.nextLong();
			st[i]=st[i-1]+t[i];
		}
		t[n+1]=Integer.MAX_VALUE;
		st[n+1]=st[n]+t[n+1];
		Arrays.fill(resa, 0);		Arrays.fill(resb, 0);
		for (i=1;i<=n;i++) {
			j=i;
			if (v[i]<=t[i]) {
				resb[i]+=v[i];
				continue;
			}
			int l=i,r=n,md;
			while (l<=r) {
				md=(l+r)/2;
				if (st[md]-st[i-1]<=v[i]) {
					j=Math.max(j, md);
					l=md+1;
				}else
					r=md-1;
			}
			resa[i]++; resa[j+1]--;
			resb[j+1]+=(v[i]-(st[j]-st[i-1]));
		}
		for (i=1;i<=n;i++) {
			resa[i]+=resa[i-1];
			printer.print(((resa[i]*t[i])+resb[i])+" ");
		}
	}
	public static void main(String[] args)throws Exception{
		MainMethod();
		printer.close();
	}
	static void halt(){
		printer.close();
		System.exit(0);
	}
	static PrintWriter printer=new PrintWriter(new OutputStreamWriter(System.out));
	static class reader{
		static BufferedReader bReader=new BufferedReader(new InputStreamReader(System.in));
		static StringTokenizer token=new StringTokenizer("");
		static String readNextLine() throws Exception{
			return bReader.readLine();
		}
		static String next() throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return token.nextToken();
		}
		static int nextInt()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Integer.parseInt(token.nextToken());
		}
		static long nextLong()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Long.parseLong(token.nextToken());
		}
		static double nextDouble()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Double.parseDouble(token.nextToken());
		}
	}
	static class MyMathCompute{
		static long [][] MatrixMultiplyMatrix(long [][] A, long [][] B, long mod) throws Exception{
			int n=A.length, m=B[0].length; 
			int p=A[0].length;
			int i,j,k;
			if (B.length!=p) throw new Exception("invalid matrix input");
			long [][] res=new long [n][m];
			for (i=0;i<n;i++) for (j=0;j<m;j++){
				if (A[i].length!=p) throw new Exception("invalid matrix input");
				res[i][j]=0;
				for (k=0;k<p;k++)
					res[i][j]=(res[i][j]+((A[i][k]*B[k][j])% mod))% mod;
			}
			return res;
		}
		static double [][] MatrixMultiplyMatrix(double [][] A, double [][] B ) throws Exception{
			int n=A.length, m=B[0].length; 
			int p=A[0].length;
			int i,j,k;
			if (B.length!=p) throw new Exception("invalid matrix input");
			double [][] res=new double [n][m];
			for (i=0;i<n;i++) for (j=0;j<m;j++){
				if (A[i].length!=p) throw new Exception("invalid matrix input");
				res[i][j]=0;
				for (k=0;k<p;k++)
					res[i][j]=res[i][j]+(A[i][k]*B[k][j]);
			}
			return res;
		}
		static long [][] MatrixPow(long [][] A,long n, long mod) throws Exception{
			if (n==1) return A;
			long [][] res=MatrixPow(A, n/2, mod);
			res=MatrixMultiplyMatrix(res, res, mod);
			if ((n % 2) == 1) res=MatrixMultiplyMatrix(A,res, mod);		
			return res;
		}
		static double [][] MatrixPow(double [][] A,long n) throws Exception{
			if (n==1) return A;
			double[][] res=MatrixPow(A, n/2);
			res=MatrixMultiplyMatrix(res, res);
			if ((n % 2) == 1) res=MatrixMultiplyMatrix(A,res);		
			return res;
		}
		static long pow(long a,long n,long mod){
			a= a % mod;
			if (n==0) return 1;
			long k=pow(a,n/2,mod);
			if ((n % 2)==0) return ((k*k)%mod);
			else return (((k*k) % mod)*a) % mod;
		}
		static double pow(double a,long n){
			if (n==0) return 1;
			double k=pow(a,n/2);
			if ((n % 2)==0) return (k*k);
			else return (((k*k) )*a) ;
		}
	}
}
