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.
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 5;
int n;
vector<long long> piles;
vector<long long> melt;
vector<long long> melt_initial;
vector<long long> cnt;
vector<long long> alone;
int main() {
  cin >> n;
  cnt.resize(n + 2, 0);
  alone.resize(n + 2, 0);
  for (int i = 0; i < n; i++) {
    long long temp;
    cin >> temp;
    piles.push_back(temp);
  }
  for (int i = 0; i < n; i++) {
    long long temp;
    cin >> temp;
    melt.push_back(temp);
    melt_initial.push_back(temp);
  }
  for (int i = 1; i < n; i++) melt[i] += melt[i - 1];
  for (int i = 0; i < n; i++) {
    long long before_melt = i == 0 ? 0 : melt[i - 1];
    long long max_melt = before_melt + piles[i];
    if (melt_initial[i] > piles[i]) {
      alone[i] += piles[i];
      continue;
    }
    int l = i, r = n - 1;
    while (r - l > 1) {
      int m = (l + r) / 2;
      if (melt[m] > max_melt)
        r = m;
      else
        l = m;
    }
    int index;
    if (melt[l] <= max_melt) index = l;
    if (melt[r] <= max_melt) index = r;
    cnt[i]++;
    cnt[index + 1]--;
    long long alone_left = piles[i];
    if (i == 0)
      alone_left -= melt[index];
    else
      alone_left -= melt[index] - melt[i - 1];
    alone[index + 1] += alone_left;
  }
  long long delta = 0;
  for (int i = 0; i < n; i++) {
    delta += cnt[i];
    long long current = alone[i] + melt_initial[i] * delta;
    cout << current << " ";
  }
  cout << endl;
  return 0;
}
