#include <bits/stdc++.h>
using namespace std;
long check(long long b[], long long e, long long x) {
  long s = 0, m;
  if (x >= b[e - 1]) return e - 1;
  while (s <= e) {
    m = (s + e) / 2;
    if (b[m] <= x && b[m + 1] > x)
      return m;
    else if (b[m] < x)
      s = m + 1;
    else
      e = m - 1;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, a[100009], b[100009], c[100009] = {0}, d[100009] = {0},
                                     e[100009] = {0};
  cin >> n;
  for (long i = long(1); i < long(n + 1); i++) cin >> a[i];
  a[0] = b[0] = 0;
  for (long i = long(1); i < long(n + 1); i++) {
    cin >> b[i];
    e[i] = b[i];
    b[i] += b[i - 1];
  }
  for (long i = long(1); i < long(n + 1); i++) {
    long x = check(b, n + 1, a[i] + b[i - 1]);
    c[x + 1] -= 1;
    d[x + 1] += (-1ll * (b[x] - (a[i] + b[i - 1])));
  }
  long p = 0;
  for (long i = long(1); i < long(n + 1); i++) {
    p += c[i];
    c[i] = i + p;
    cout << c[i] * e[i] + d[i] << " ";
  }
}

### Prompt

In Cpp, your task is to solve the following problem:

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;
long check(long long b[], long long e, long long x) {
  long s = 0, m;
  if (x >= b[e - 1]) return e - 1;
  while (s <= e) {
    m = (s + e) / 2;
    if (b[m] <= x && b[m + 1] > x)
      return m;
    else if (b[m] < x)
      s = m + 1;
    else
      e = m - 1;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, a[100009], b[100009], c[100009] = {0}, d[100009] = {0},
                                     e[100009] = {0};
  cin >> n;
  for (long i = long(1); i < long(n + 1); i++) cin >> a[i];
  a[0] = b[0] = 0;
  for (long i = long(1); i < long(n + 1); i++) {
    cin >> b[i];
    e[i] = b[i];
    b[i] += b[i - 1];
  }
  for (long i = long(1); i < long(n + 1); i++) {
    long x = check(b, n + 1, a[i] + b[i - 1]);
    c[x + 1] -= 1;
    d[x + 1] += (-1ll * (b[x] - (a[i] + b[i - 1])));
  }
  long p = 0;
  for (long i = long(1); i < long(n + 1); i++) {
    p += c[i];
    c[i] = i + p;
    cout << c[i] * e[i] + d[i] << " ";
  }
}

```