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.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Xorq {

	static class FastReader {

		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static int n;
	static int a[]=new int[100010],t[]=new int[100010];
	static long ans,cf[] = new long[100010],tot[]=new long[100010],sum[]=new long[100010];
	public static void main(String[] args) throws IOException {
		FastReader sc = new FastReader();
		 n = sc.nextInt();
		for (int i = 1; i <=n; i++)
			a[i] = sc.nextInt();
		for(int i=1;i<=n;i++){
			t[i]=sc.nextInt();
			sum[i]=sum[i-1]+t[i];
		}
		
		
		for(int i=1;i<=n;i++){
			int l=i,r=n;
			ans=i-1;
			while(l<=r){
				int mid = l+r>>1;
			if(sum[mid]-sum[i-1]<=a[i]){
				ans=mid;
				l=mid+1;
			} else{
				r=mid-1;
			}
			}
			ans++;
			cf[i]++;
			cf[(int) ans]--;
			tot[(int) ans]+=a[i]-sum[(int) (ans)-1]+sum[i-1];
		}
		for (int i=1;i<=n;i++) cf[i]+=cf[i-1];
		for(int i=1;i<=n;i++)
			System.out.print(cf[i]*t[i]+tot[i]+" ");
	}
}