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 int MaxN = 200 * 1000;
  const int MaxVal = 300 * 1000 + 1;
  struct MyPair {
    int first;
    long long second;
  };
  MyPair tCountSum[4 * MaxVal];
  MyPair CountSumNumbers(int v, int tl, int tr, int l, int r) {
    if (l > r) return {0, 0};
    if (l == tl && r == tr) {
      return tCountSum[v];
    }
    int mid = (tl + tr) / 2;
    auto left = CountSumNumbers(v * 2, tl, mid, l, min(r, mid));
    auto right = CountSumNumbers(v * 2 + 1, mid + 1, tr, max(l, mid + 1), r);
    return {left.first + right.first, left.second + right.second};
  }
  int CountNumbers(int l, int r) {
    if (l > r) return 0;
    l = max(l, 0);
    r = min(r, MaxVal - 1);
    return CountSumNumbers(1, 0, MaxVal - 1, l, r).first;
  }
  long long SumNumbers(int l, int r) {
    if (l > r) return 0;
    l = max(l, 0);
    r = min(r, MaxVal - 1);
    return CountSumNumbers(1, 0, MaxVal - 1, l, r).second;
  }
  MyPair CountSumNumbers(int l, int r) {
    if (l > r) return {0, 0};
    l = max(l, 0);
    r = min(r, MaxVal - 1);
    return CountSumNumbers(1, 0, MaxVal - 1, l, r);
  }
  void AddNumber(int v, int tl, int tr, int val) {
    if (tl == tr) {
      tCountSum[v].first++;
      tCountSum[v].second += val;
      return;
    }
    int mid = (tl + tr) / 2;
    if (val <= mid) {
      AddNumber(v * 2, tl, mid, val);
    } else {
      AddNumber(v * 2 + 1, mid + 1, tr, val);
    }
    tCountSum[v].first = tCountSum[v * 2].first + tCountSum[v * 2 + 1].first;
    tCountSum[v].second = tCountSum[v * 2].second + tCountSum[v * 2 + 1].second;
  }
  void AddNumber(int x) { AddNumber(1, 0, MaxVal - 1, x); }
  MyPair tCountSumForward[4 * MaxVal];
  MyPair tAddForward[4 * MaxVal];
  void push(int v) {
    if (tAddForward[v].first != 0 || tAddForward[v].second != 0) {
      if (v * 2 < 4 * MaxVal) {
        tAddForward[v * 2].first += tAddForward[v].first;
        tAddForward[v * 2].second += tAddForward[v].second;
      }
      if (v * 2 + 1 < 4 * MaxVal) {
        tAddForward[v * 2 + 1].first += tAddForward[v].first;
        tAddForward[v * 2 + 1].second += tAddForward[v].second;
      }
      tCountSumForward[v].first += tAddForward[v].first;
      tCountSumForward[v].second += tAddForward[v].second;
      tAddForward[v].first = 0;
      tAddForward[v].second = 0;
    }
  }
  MyPair GetCountSumForward(int v, int tl, int tr, int pos) {
    if (tl == tr) {
      push(v);
      return tCountSumForward[v];
    }
    push(v);
    int mid = (tl + tr) / 2;
    if (pos <= mid)
      return GetCountSumForward(v * 2, tl, mid, pos);
    else
      return GetCountSumForward(v * 2 + 1, mid + 1, tr, pos);
  }
  MyPair GetCountSumForward(int val) {
    if (val < 0 || val >= MaxVal) return {0, 0};
    return GetCountSumForward(1, 0, MaxVal - 1, val);
  }
  void AddGetValueForward(int v, int tl, int tr, int l, int r, int addSum) {
    if (l > r) return;
    if (l == tl && r == tr) {
      tAddForward[v].first++;
      tAddForward[v].second += addSum;
      push(v);
      return;
    }
    push(v);
    int mid = (tl + tr) / 2;
    AddGetValueForward(v * 2, tl, mid, l, min(r, mid), addSum);
    AddGetValueForward(v * 2 + 1, mid + 1, tr, max(l, mid + 1), r, addSum);
    tCountSumForward[v].first =
        tCountSumForward[v * 2].first + tCountSumForward[v * 2 + 1].first;
    tCountSumForward[v].second =
        tCountSumForward[v * 2].second + tCountSumForward[v * 2 + 1].second;
  }
  void AddGetValueForward(int l, int r, int addSum) {
    l = max(l, 0);
    r = min(r, MaxVal - 1);
    AddGetValueForward(1, 0, MaxVal - 1, l, r, addSum);
  }
  bool used[MaxVal];
  MyPair forw[MaxVal];
  int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    vector<int> a(n);
    vector<long long> res(n, 0);
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }
    for (int i = 0; i < n; ++i) {
      res[i] += a[i] * 1ll * CountNumbers(a[i] + 1, MaxVal);
      res[i] += SumNumbers(1, a[i] - 1);
      auto tmp2 = GetCountSumForward(a[i]);
      res[i] += a[i] * 1ll * tmp2.first - tmp2.second;
      res[i] += a[i] * 1ll * forw[a[i]].first - forw[a[i]].second;
      if (a[i] <= 100) {
        for (int mult = 1; a[i] * mult <= MaxVal; ++mult) {
          int temp = a[i] * mult;
          for (int x = a[i] * mult; x < min(MaxVal, a[i] * (mult + 1)); ++x) {
            if (used[x]) {
              res[i] += x - temp;
            }
            forw[x].first++;
            forw[x].second += temp;
          }
        }
      } else {
        for (int mult = 1; a[i] * mult <= MaxVal; ++mult) {
          auto tmp = CountSumNumbers(a[i] * mult, a[i] * (mult + 1) - 1);
          res[i] += tmp.second - a[i] * 1ll * mult * tmp.first;
          AddGetValueForward(a[i] * mult, a[i] * (mult + 1) - 1, a[i] * mult);
        }
      }
      AddNumber(a[i]);
      used[a[i]] = true;
      if (i > 0) res[i] += res[i - 1];
    }
    for (int i = 0; i < n; ++i) cout << res[i] << " ";
    cout << endl;
    return 0;
  }
  