#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long n;
  cin >> n;
  vector<long long> a(n + 1), temps(n + 1, 0);
  for (long long i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1; i <= n; i++) cin >> temps[i], temps[i] += temps[i - 1];
  vector<long long> f(n + 2), m(n + 2);
  for (long long i = 1; i <= n; i++) {
    long long lo = i, hi = n, take = n + 1;
    while (lo <= hi) {
      long long mid = (lo + hi) / 2;
      if (temps[mid] - temps[i - 1] > a[i]) {
        take = mid;
        hi = mid - 1;
      } else {
        lo = mid + 1;
      }
    }
    f[i]++;
    f[take]--;
    if (take > i)
      m[take] += a[i] - (temps[take - 1] - temps[i - 1]);
    else
      m[take] += a[i];
  }
  for (long long i = 1; i <= n; i++) {
    f[i] += f[i - 1];
    cout << f[i] * (temps[i] - temps[i - 1]) + m[i] << ' ';
  }
}

### Prompt

Develop a solution in Cpp to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long n;
  cin >> n;
  vector<long long> a(n + 1), temps(n + 1, 0);
  for (long long i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1; i <= n; i++) cin >> temps[i], temps[i] += temps[i - 1];
  vector<long long> f(n + 2), m(n + 2);
  for (long long i = 1; i <= n; i++) {
    long long lo = i, hi = n, take = n + 1;
    while (lo <= hi) {
      long long mid = (lo + hi) / 2;
      if (temps[mid] - temps[i - 1] > a[i]) {
        take = mid;
        hi = mid - 1;
      } else {
        lo = mid + 1;
      }
    }
    f[i]++;
    f[take]--;
    if (take > i)
      m[take] += a[i] - (temps[take - 1] - temps[i - 1]);
    else
      m[take] += a[i];
  }
  for (long long i = 1; i <= n; i++) {
    f[i] += f[i - 1];
    cout << f[i] * (temps[i] - temps[i - 1]) + m[i] << ' ';
  }
}

```