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 long long mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m, k, l, i, j, test = 1, t, x, y, z, a, b, c, p, q, r, u, v, w;
  while (test--) {
    cin >> n;
    vector<long long> ice(n), temp(n), sum(n), res(n, 0), ans(n + 1, 0);
    for (i = (0); i < (n); ++i) cin >> ice[i];
    for (i = (0); i < (n); ++i) cin >> temp[i];
    sum[0] = temp[0];
    for (i = (1); i < (n); ++i) sum[i] = sum[i - 1] + temp[i];
    x = 0;
    for (i = (0); i < (n); ++i) {
      p = lower_bound(sum.begin(), sum.end(), ice[i] + x) - sum.begin();
      if (p == n) {
        ans[i]++;
        ans[p]--;
      } else if (sum[p] == ice[i] + x) {
        ans[i]++;
        ans[p + 1]--;
      } else {
        if (p == 0)
          res[p] += ice[i] + x;
        else {
          ans[i]++;
          ans[p]--;
          res[p] += ice[i] + x - sum[p - 1];
        }
      }
      x = sum[i];
    }
    for (i = (1); i < (n); ++i) ans[i] += ans[i - 1];
    for (i = (0); i < (n); ++i) cout << ans[i] * temp[i] + res[i] << " ";
    cout << "\n";
  }
  return 0;
}
