#include <bits/stdc++.h>
using namespace std;
const int mxn = 3e5 + 5;
const long long MOD = 1e9 + 7;
const int BASE = 100000000;
const int INF = 1e9 + 8;
long long g[mxn], cnt[mxn], a[mxn];
void up_g(int x, const long long &val) {
  while (x < mxn) {
    g[x] += val;
    x += x & (-x);
  }
}
void update_g(int l, int r, const long long &val) {
  up_g(l, val);
  up_g(r + 1, -val);
}
long long get_g(int x) {
  long long res = 0;
  while (x) {
    res += g[x];
    x -= x & (-x);
  }
  return res;
}
void update_cnt(int x) {
  while (x < mxn) {
    cnt[x] += 1LL;
    x += x & (-x);
  }
}
long long get(int x) {
  long long res = 0;
  while (x) {
    res += cnt[x];
    x -= x & (-x);
  }
  return res;
}
long long get_cnt(int l, int r) { return (get(r) - get(l - 1)); }
signed main() {
  int n;
  cin >> n;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  long long cur = 0, sum = 0;
  for (int i = (1); i <= (n); ++i) {
    cur += (long long)(i - 1) * a[i] - get_g(a[i]);
    cur += sum;
    int x = (int)(a[i]);
    while (x < mxn) {
      long long k = min(x + (int)(a[i]) - 1, (int)(mxn - 5));
      cur -= (long long)(x)*get_cnt(x, k);
      update_g(x, k, x);
      x += a[i];
    }
    update_cnt(a[i]);
    sum += a[i];
    cout << cur << ' ';
  }
}

### Prompt

Please provide a CPP coded solution to the problem described below:

You have an array a consisting of n distinct positive integers, numbered from 1 to n. Define p_k as $$$p_k = ∑_{1 ≤ i, j ≤ k} a_i mod a_j, where x \bmod y denotes the remainder when x is divided by y. You have to find and print p_1, p_2, \ldots, p_n$$$. 

Input

The first line contains n — the length of the array (2 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n space-separated distinct integers a_1, …, a_n (1 ≤ a_i ≤ 3 ⋅ 10^5, a_i ≠ a_j if i ≠ j). 

Output

Print n integers p_1, p_2, …, p_n. 

Examples

Input


4
6 2 7 3


Output


0 2 12 22


Input


3
3 2 1


Output


0 3 5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int mxn = 3e5 + 5;
const long long MOD = 1e9 + 7;
const int BASE = 100000000;
const int INF = 1e9 + 8;
long long g[mxn], cnt[mxn], a[mxn];
void up_g(int x, const long long &val) {
  while (x < mxn) {
    g[x] += val;
    x += x & (-x);
  }
}
void update_g(int l, int r, const long long &val) {
  up_g(l, val);
  up_g(r + 1, -val);
}
long long get_g(int x) {
  long long res = 0;
  while (x) {
    res += g[x];
    x -= x & (-x);
  }
  return res;
}
void update_cnt(int x) {
  while (x < mxn) {
    cnt[x] += 1LL;
    x += x & (-x);
  }
}
long long get(int x) {
  long long res = 0;
  while (x) {
    res += cnt[x];
    x -= x & (-x);
  }
  return res;
}
long long get_cnt(int l, int r) { return (get(r) - get(l - 1)); }
signed main() {
  int n;
  cin >> n;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  long long cur = 0, sum = 0;
  for (int i = (1); i <= (n); ++i) {
    cur += (long long)(i - 1) * a[i] - get_g(a[i]);
    cur += sum;
    int x = (int)(a[i]);
    while (x < mxn) {
      long long k = min(x + (int)(a[i]) - 1, (int)(mxn - 5));
      cur -= (long long)(x)*get_cnt(x, k);
      update_g(x, k, x);
      x += a[i];
    }
    update_cnt(a[i]);
    sum += a[i];
    cout << cur << ' ';
  }
}

```