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;
long long n, x, a, b, sum = 100005, mx, p, m, dif, k;
vector<long long> big, small, v, V, T;
vector<vector<int> > vv;
bool ano = false;
long long prefix[100005];
multiset<int> st;
string second;
int binary(int a) {
  a++;
  int zac = a;
  int kon = n + 1;
  int mid = (zac + kon) / 2;
  while (kon - zac > 1) {
    if (prefix[mid] - prefix[a - 1] > V[a - 1]) {
      kon = mid;
    } else {
      zac = mid;
    }
    mid = (zac + kon) / 2;
  }
  return mid;
}
int main() {
  std::ios::sync_with_stdio(false);
  cin >> n;
  long long day[n + 1], pos[n];
  bool block[n];
  for (int i = 0; i < n; i++) {
    cin >> x;
    V.push_back(x);
    block[i] = false;
    day[i] = 0;
  }
  day[n] = 0;
  for (int i = 0; i < n; i++) {
    cin >> x;
    T.push_back(x);
    if (i == 0) {
      prefix[i] = 0;
    }
    prefix[i + 1] = prefix[i] + x;
  }
  for (int i = 0; i < n; i++) {
    if (V[i] >= T[i]) {
      pos[i] = binary(i);
      day[pos[i] + 1] += (V[i] - (prefix[pos[i]] - prefix[i]));
    } else {
      day[i + 1] += V[i];
      block[i] = true;
    }
  }
  vector<pair<long long, long long> > par;
  pair<long long, long long> tmp;
  for (int i = 0; i < n; i++) {
    if (block[i]) {
      continue;
    }
    tmp.first = i + 1;
    tmp.second = -1;
    par.push_back(tmp);
    tmp.first = pos[i] + 1;
    tmp.second = 1;
    par.push_back(tmp);
  }
  if (par.size() > 0) {
    sort(par.begin(), par.end());
    long long cnt = 0;
    long long ps = 0;
    for (int i = 1; i <= n; i++) {
      while (par[ps].first == i) {
        if (par[ps].second == -1) {
          cnt++;
        } else {
          cnt--;
        }
        ps++;
      }
      day[i] += (cnt * T[i - 1]);
    }
  }
  for (int i = 1; i <= n; i++) {
    cout << day[i] << " ";
  }
  cout << endl;
}
