description: 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
solution: #include <bits/stdc++.h>
  using namespace std;
  const double eps = 1e-7;
  const double PI = acos(-1);
  const int MOD = 998244353;
  const int INF = 0x3f3f3f3f;
  const int N = 3e5 + 7;
  int n, m;
  int a[N], p[N];
  long long res;
  template <typename T>
  struct SegmentTree {
    int sz;
    T tr[N << 2], lazy[N << 2], cnt[N << 2];
    SegmentTree() {}
    void build(const int &n, const T &k = 0) {
      sz = n;
      _build(1, n, k);
    }
    void modify(const int &x, const T &k) { _modify(x, k, 1, sz); }
    void add(const int &x, const T &k) { _add(x, x, k, 1, sz); }
    void add(int l, int r, const T &k) {
      if (l > r) swap(l, r);
      _add(l, r, k, 1, sz);
    }
    void mark(const int &x) { mark(x, 1, sz, 1); }
    T query(const int &x) { return _query(x, x, 1, sz); }
    T query(int l, int r) {
      if (l > r) swap(l, r);
      return _query(l, r, 1, sz);
    }
  
   private:
    void mark(int x, int l, int r, int i = 1) {
      if (l == r) {
        ++cnt[i];
        return;
      }
      int mid = (l + r) >> 1;
      if (x <= mid)
        mark(x, l, mid, i << 1);
      else
        mark(x, mid + 1, r, i << 1 | 1);
      push_up(i);
    }
    void push_up(const int &i) {
      tr[i] = tr[i << 1] + tr[i << 1 | 1];
      cnt[i] = cnt[i << 1] + cnt[i << 1 | 1];
    }
    void push_down(const int &i, const int &len) {
      if (!lazy[i]) return;
      tr[i << 1] += lazy[i] * (len - len / 2);
      tr[i << 1 | 1] += lazy[i] * (len / 2);
      lazy[i << 1] += lazy[i];
      lazy[i << 1 | 1] += lazy[i];
      lazy[i] = 0;
    }
    void _build(const int &l, const int &r, const T &k = 0, const int &i = 1) {
      lazy[i] = 0;
      cnt[i] = 0;
      if (l == r) {
        tr[i] = k;
        return;
      }
      int mid = (l + r) >> 1;
      _build(l, mid, k, i << 1);
      _build(mid + 1, r, k, i << 1 | 1);
      push_up(i);
    }
    void _modify(const int &x, const T &k, const int &trl, const int &trr,
                 const int &i = 1) {
      if (trl == x && trr == x) {
        tr[i] = k;
        lazy[i] = 0;
        return;
      }
      push_down(i, trr - trl + 1);
      int mid = (trl + trr) >> 1;
      if (x <= mid)
        _modify(x, k, trl, mid, i << 1);
      else
        _modify(x, k, mid + 1, trr, i << 1 | 1);
      push_up(i);
    }
    void _add(const int &l, const int &r, const T &k, const int &trl,
              const int &trr, const int &i = 1) {
      if (trl >= l && trr <= r) {
        tr[i] += k * (trr - trl + 1);
        lazy[i] += k;
        res -= k * cnt[i];
        return;
      }
      push_down(i, trr - trl + 1);
      int mid = (trl + trr) >> 1;
      if (l <= mid) _add(l, r, k, trl, mid, i << 1);
      if (r > mid) _add(l, r, k, mid + 1, trr, i << 1 | 1);
      push_up(i);
    }
    T _query(const int &l, const int &r, const int &trl, const int &trr,
             const int &i = 1) {
      if (trl >= l && trr <= r) return tr[i];
      push_down(i, trr - trl + 1);
      int mid = (trl + trr) >> 1;
      T res = 0;
      if (l <= mid) res += _query(l, r, trl, mid, i << 1);
      if (r > mid) res += _query(l, r, mid + 1, trr, i << 1 | 1);
      return res;
    }
  };
  SegmentTree<long long> tree;
  inline void solve() {
    cin >> n;
    for (int i = 1; i <= n; ++i) {
      cin >> a[i];
      m = max(a[i], m);
    }
    tree.build(m);
    res = 0;
    long long presum = 0;
    for (int i = 1; i <= n; ++i) {
      for (int j = a[i]; j <= m; j += a[i]) {
        tree.add(j, min(m, j + a[i] - 1), j);
      }
      res += 1ll * i * a[i] + presum - tree.query(a[i]);
      presum += a[i];
      tree.mark(a[i]);
      cout << res << " \n"[i == n];
    }
  }
  signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int T = 1;
    for (int t = 1; t <= T; ++t) {
      solve();
    }
    return 0;
  }
  