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 int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long LL_INF = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1);
const double EPS = 1e-10;
const int N = 100010;
int n;
long long v[N];
long long t[N];
int a[N], b[N];
long long dp[N];
long long res[N];
int lowerBound(long long key, int pos) {
  int res = -1, low = pos, high = n;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (dp[mid] - dp[pos - 1] >= key) {
      res = mid;
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> v[i];
  }
  for (int i = 1; i <= n; ++i) {
    cin >> t[i];
  }
  for (int i = 1; i <= n; ++i) {
    dp[i] = dp[i - 1] + t[i];
  }
  for (int i = 1; i <= n; ++i) {
    int pos = lowerBound(v[i], i);
    if (pos == -1) {
      ++b[i];
      --b[n + 1];
      continue;
    }
    ++b[i];
    --b[pos];
    long long melt = dp[pos - 1] - dp[i - 1];
    long long remain = v[i] - melt;
    res[pos] += remain;
  }
  for (int i = 1; i <= n; ++i) {
    a[i] = b[i] + a[i - 1];
  }
  for (int i = 1; i <= n; ++i) {
    res[i] += t[i] * a[i];
    cout << res[i] << ' ';
  }
}
