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;

public class ProblemC {
  public static void main(String[] args)throws IOException {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(reader.readLine());
    String[] strs = reader.readLine().split(" ");
    int[] v = new int[n];
    for(int i = 0; i < n; i++){
      v[i] = Integer.parseInt(strs[i]);
    }
    strs = reader.readLine().split(" ");
    long[] t = new long[n];
    long[] sum = new long[n];
    for(int i = 0; i < n; i++){
      t[i] = Long.parseLong(strs[i]);
      sum[i] = t[i];
      if(i > 0){
        sum[i] += sum[i - 1];
      }
    }
    int[] runnerUpdate = new int[n + 1];
    long[] remainderUpdate = new long[n + 1];
    for(int i = 0; i < n; i++){
      if(t[i] > v[i]){
        remainderUpdate[i] += v[i];
        continue;
      }
      int idx = binSearch(v[i], i, sum);
      runnerUpdate[i] += 1;
      runnerUpdate[idx] -= 1;
      long rem = sum[idx - 1];
      if(i > 0){
        rem -= sum[i - 1];
      }
      remainderUpdate[idx] += v[i] - (int) rem;
    }
    for(int i = 0; i < n; i++){
      if(i > 0){
        runnerUpdate[i] += runnerUpdate[i - 1];
      }
      long res = 1L * t[i] * runnerUpdate[i] + remainderUpdate[i];
      System.out.print(res + " ");
    }
    System.out.println();
  }

  private static int binSearch(int value, int from, long[] sum){
    long subtract = 0;
    if(from > 0){
      subtract = sum[from - 1];
    }
    int low = from;
    int high = sum.length - 1;
    while(low <= high){
      int mid = (low + high) / 2;
      long consecutiveSum = sum[mid] - subtract;
      if(consecutiveSum <= value){
        low = mid + 1;
      }else{
        high = mid - 1;
      }
    }
    return low;
  }
}
