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;
int main() {
  long long n;
  cin >> n;
  long long arr[n];
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  vector<long long> t, pref;
  long long num;
  cin >> num;
  t.push_back(num);
  pref.push_back(num);
  for (long long i = 1; i < n; i++) {
    cin >> num;
    t.push_back(num);
    pref.push_back(pref[i - 1] + num);
  }
  long long day[n], ans[n];
  for (long long i = 0; i < n; i++) {
    num = arr[i];
    if (i > 0) num += pref[i - 1] + (arr[i] == 0);
    auto it = lower_bound(pref.begin(), pref.end(), num);
    day[i] = distance(pref.begin(), it) + 1;
    ans[i] = 0;
  }
  map<long long, long long> mp;
  long long c = 0;
  for (long long i = 0; i < n; i++) {
    num = arr[i];
    if (i > 0) num += pref[i - 1] + (arr[i] == 0);
    auto it = lower_bound(pref.begin(), pref.end(), num);
    if (it == pref.end()) continue;
    if (it != pref.begin()) {
      it--;
      ans[day[i] - 1] += (num - *it - (arr[i] == 0));
    } else
      ans[day[i] - 1] += arr[i];
  }
  for (long long i = 0; i < n; i++) {
    mp[day[i]]++;
    c++;
    c -= mp[i + 1];
    ans[i] += c * t[i];
  }
  for (long long i = 0; i < n; i++) cout << ans[i] << " ";
}
