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 class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.flush();out.close();
    }
        static class TaskE {
         class pair{
          long v;int id;pair(long a,int b){v=a;id=b;}
         }
         public void solve(int testNumber, InputReader in, PrintWriter out) {
             int n=in.nextInt();
             long v[]=new long[n];for(int i=0;i<n;i++)v[i]=in.nextLong();
             TreeSet<pair> ts=new TreeSet<>(new Comparator<pair>(){
              public int compare(pair p1,pair p2){
               return p1.v==p2.v?p1.id-p2.id:Long.compare(p1.v,p2.v);
              }
             });
             long T[]=new long[n+1];
             long pT[]=new long[n+1];
             for(int i=1;i<=n;i++)pT[i]=pT[i-1]+(T[i]=in.nextLong());
             for(int i=0;i<n;i++){
              ts.add(new pair(pT[i+1],i+1));
             }
             int ans[]=new int[n+10];
             long vx[]=new long[n+10];
             for(int i=0;i<n;i++){
              pair p=ts.ceiling(new pair(v[i]+pT[i],-1));
              if(p!=null){
               if(p.v!=v[i]){vx[p.id]+=v[i]-pT[p.id-1]+pT[i];ans[p.id]++;}
               else ans[p.id+1]++;
              }
             }for(int i=1;i<=n;i++)ans[i]+=ans[i-1];
             for(int i=1;i<=n;i++){
              vx[i]+=(i-ans[i])*T[i];
             }
             for(int i=1;i<=n;i++)out.print(vx[i]+" ");
         }
         /*pair ja[][];long w[];int from[],to[],c[];
             void make(int n,int m,InputReader in){
              ja=new pair[n+1][];w=new long[m];from=new int[m];to=new int[m];c=new int[n+1];
              for(int i=0;i<m;i++){
               int u=in.nextInt(),v=in.nextInt();long wt=in.nextLong();
               c[u]++;c[v]++;from[i]=u;to[i]=v;w[i]=wt;
              }
              for(int i=1;i<=n;i++){
               ja[i]=new pair[c[i]];c[i]=0;
              }
              for(int i=0;i<m;i++){
               ja[from[i]][c[from[i]]++]=new pair(to[i],w[i]);
               ja[to[i]][c[to[i]]++]=new pair(from[i],w[i]);
              }
             }*/
        int[] radixSort(int[] f){ return radixSort(f, f.length); }
	int[] radixSort(int[] f, int n)
	{
		int[] to = new int[n];
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(f[i]&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[f[i]&0xffff]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(f[i]>>>16)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[f[i]>>>16]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		return f;
	}
    }
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;
        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
            st = null;
        }

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

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}