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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    long MOD = 1000000007L;
    int INF = 1000000000;
    int[] dX = new int[]{-1, 0, 1, 0};
    int[] dY = new int[]{0, 1, 0, -1};
    
    public class Obj implements Comparable<Obj>{
        public int start;
        public int end;
        
        public Obj(int start_, int end_){
            this.start = start_;
            this.end = end_;

        }
        
        public int compareTo(Obj other){
            if (other.start == this.start){
                return this.end - other.end;
            }
            return this.start - other.start;
        }

    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
        Codechef cf = new Codechef();
        cf.Solve();
	}
	
	public void Solve(){
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        long[] V = new long[n];
        long[] T = new long[n];
        long[] dp = new long[n];
        int[] cnt = new int[n];
        long[] Drop = new long[n];
        for (int i = 0; i < n; ++i){
            V[i] = sc.nextLong();
        }
        for (int i = 0; i < n; ++i){
            T[i] = sc.nextLong();
            dp[i] = T[i];
            if (i > 0){
                dp[i] += dp[i-1];
            }
        }
        
        for (int i = 0; i < n; ++i){
            cal(i, n, V, dp, cnt, T, Drop);
        }
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int curCount = 0;
        for (int i = 0; i < n; ++i){
        	curCount += cnt[i];
            long res = T[i] * (1 + i - curCount) - Drop[i];
            // System.out.println("cnt[" + i + "]:"  + cnt[i]);
            out.print(res + " ");
        }
        out.close();
	}
	
	private void cal(int index, int n, long[] V, long[] dp, int[] cnt, long[] T, long[] Drop){
		// System.out.println("index: " + index);
	    int lo = index;
	    int hi = n-1;
	    int best = lo - 1;
	    long lost = 0L;
	    while (lo <= hi){
	        int mid = lo + (hi - lo) / 2;
	        //System.out.println(mid);
	        long cur = dp[mid];
	        if (index > 0){
	            cur -= dp[index-1];
	        }
	        if (cur < V[index]){
	            best = mid;
	            lo = mid + 1;
	            lost = cur;
	            // System.out.println(mid + " lost: " + lost + " " + dp[mid]);
	        }else{
	            hi = mid - 1;
	        }
	    }
	    //System.out.println(index + " V[index]: " + V[index] + " " + best + " lost: " + lost);
	    best++;
	    if (best < n){
	    	long sum = V[index] - lost;
	        Drop[best] += T[best] - V[index] + lost;
	        //System.out.println(best + " sum: " + sum +  " tmp: " + T[best] +  " Drop: " + Drop[best]);
	    }
	    best++;
	    if (best < n){
	        cnt[best]++;
	    }
	}
	
	
	//-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         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;
      }

   }
}
