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 int MOD = 1e9 + 7;
bool IsPowerOfTwo(long long int x) { return (x != 0) && ((x & (x - 1)) == 0); }
long long int poer(long long int a, long long int b) {
  long long int rs = 1;
  while (b > 0) {
    if (b & 1) rs *= a;
    a *= a;
    b /= 2;
  }
  return rs;
}
long long int mod_poer(long long int a, long long int b, long long int mo) {
  long long int rs = 1;
  while (b > 0) {
    if (b & 1) rs = (rs * a) % mo;
    a = (a * a) % mo;
    b /= 2;
  }
  return rs % mo;
}
long long int d, x, y;
void ext_euclid(long long int a, long long int b) {
  if (b == 0) {
    d = a;
    x = 1;
    y = 0;
  } else {
    ext_euclid(b, a % b);
    long long int temp = x;
    x = y;
    y = temp - (a / b) * y;
  }
}
long long int mod_inverse1(long long int a, long long int m) {
  ext_euclid(a, m);
  return (x % m + m) % m;
}
long long int mod_inverse2(long long int a, long long int m) {
  return mod_poer(a, m - 2, m);
}
long long int gcd(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long int fact[200005];
void fac() {
  fact[1] = fact[0] = 1;
  for (long long int i = 2; i <= 200005; ++i) {
    fact[i] = ((fact[i - 1] % MOD) * i) % MOD;
  }
}
long long int combi(long long int a, long long int b) {
  if (b > a) return 0;
  if (b == a)
    return 1;
  else {
    long long int x = mod_poer(fact[b], MOD - 2, MOD) % MOD;
    long long int y = mod_poer(fact[a - b], MOD - 2, MOD) % MOD;
    return ((((fact[a]) * x) % MOD) * y) % MOD;
  }
}
multiset<long long int> s;
vector<long long int> v;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long int n;
  long long int suma = 0, a, b, c;
  cin >> n;
  for (long long int i = 1; i <= n; ++i) {
    cin >> a;
    v.push_back(a);
  }
  for (long long int i = 0; i < n; ++i) {
    cin >> a;
    s.insert(v[i] + suma);
    b = 0;
    auto it = s.begin();
    while (it != s.end()) {
      c = *it;
      if (c <= a + suma) {
        b += (c - suma);
        s.erase(it);
        it = s.begin();
      } else
        break;
    }
    c = s.size();
    b += a * c;
    suma += a;
    cout << b << " ";
  }
  cout << endl;
  return 0;
}
