#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T1, typename T2>
inline void chkmin(T1& x, const T2& y) {
  if (y < x) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1& x, const T2& y) {
  if (x < y) x = y;
}
const ll N = 3e5 + 10;
ll n;
ll a[N];
ll cnt[N];
struct Fenwick {
  ll n;
  vector<ll> tree;
  Fenwick() {}
  Fenwick(ll _n) {
    n = _n;
    tree.assign(n, 0);
  }
  void upd(ll pos, ll val) {
    for (; pos < n; pos |= pos + 1) {
      tree[pos] += val;
    }
  }
  ll get(ll r) {
    ll ans = 0;
    for (; r >= 0; r = (r & (r + 1)) - 1) {
      ans += tree[r];
    }
    return ans;
  }
  ll get(ll l, ll r) {
    chkmax(l, 0);
    chkmin(r, n - 1);
    if (l > r) return 0;
    return get(r) - get(l - 1);
  }
};
struct Node {
  ll modSum;
  ll modAdd;
  ll sum;
  Node() : modSum(0), modAdd(0), sum(0) {}
  Node getVal(ll sz) const {
    Node ans;
    ans.sum = sum + modSum * sz + modAdd * ((ll)sz * (sz - 1) / 2);
    return ans;
  }
};
Node merge(const Node& a, const Node& b) {
  Node ans;
  ans.sum = a.sum + b.sum;
  return ans;
}
namespace SegmentTree {
Node tree[4 * N];
ll myTree[N];
void init() {}
void push(ll v, ll szL) {
  tree[v * 2].modSum += tree[v].modSum;
  tree[v * 2].modAdd += tree[v].modAdd;
  tree[v * 2 + 1].modSum += tree[v].modSum + tree[v].modAdd * szL;
  tree[v * 2 + 1].modAdd += tree[v].modAdd;
  tree[v].modSum = 0;
  tree[v].modAdd = 0;
}
ll upd(ll v, ll tl, ll tr, ll l, ll r, ll modSum) {
  if (tl >= r || tr <= l) return 0;
  if (tl >= l && tr <= r) {
    tree[v].modAdd++;
    tree[v].modSum += modSum;
    return tr - tl;
  }
  ll tm = (tl + tr) / 2;
  push(v, tm - tl);
  ll szL = upd(v * 2, tl, tm, l, r, modSum);
  szL += upd(v * 2 + 1, tm, tr, l, r, modSum + szL);
  tree[v] = merge(tree[v * 2].getVal(tm - tl), tree[v * 2 + 1].getVal(tr - tm));
  return szL;
}
void upd(ll l, ll r) {
  chkmax(l, 0);
  chkmin(r, N - 1);
  if (l > r) return;
  upd(1, 0, N, l, r + 1, 0);
}
ll get(ll v, ll tl, ll tr, ll pos) {
  if (tl >= pos + 1 || tr <= pos) return 0;
  if (tl == tr - 1) {
    return (tree[v].getVal(tr - tl)).sum;
  }
  ll tm = (tl + tr) / 2;
  push(v, tm - tl);
  ll ans = get(v * 2, tl, tm, pos) + get(v * 2 + 1, tm, tr, pos);
  tree[v] = merge(tree[v * 2].getVal(tm - tl), tree[v * 2 + 1].getVal(tr - tm));
  return ans;
}
ll get(ll pos) { return get(1, 0, N, pos); }
};  // namespace SegmentTree
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout.precision(20), cout.setf(ios::fixed);
  Fenwick sum(N);
  Fenwick cnt(N);
  SegmentTree::init();
  cin >> n;
  for (ll i = 0; i < n; ++i) {
    cin >> a[i];
  }
  ll ans = 0;
  for (ll i = 0; i < n; ++i) {
    ans += (ll)a[i] * cnt.get(a[i] + 1, N - 1);
    ans += sum.get(0, a[i] - 1);
    ans += SegmentTree::get(a[i]);
    for (ll l = a[i], step = 1; l < N; l += a[i], ++step) {
      ll r = l + a[i] - 1;
      chkmin(r, N - 1);
      ans += sum.get(l, r) - cnt.get(l, r) * a[i] * step;
    }
    cout << ans << ' ';
    cnt.upd(a[i], 1);
    sum.upd(a[i], a[i]);
    for (ll l = a[i]; l < N; l += a[i]) {
      SegmentTree::upd(l, l + a[i] - 1);
    }
  }
  cout << '\n';
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T1, typename T2>
inline void chkmin(T1& x, const T2& y) {
  if (y < x) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1& x, const T2& y) {
  if (x < y) x = y;
}
const ll N = 3e5 + 10;
ll n;
ll a[N];
ll cnt[N];
struct Fenwick {
  ll n;
  vector<ll> tree;
  Fenwick() {}
  Fenwick(ll _n) {
    n = _n;
    tree.assign(n, 0);
  }
  void upd(ll pos, ll val) {
    for (; pos < n; pos |= pos + 1) {
      tree[pos] += val;
    }
  }
  ll get(ll r) {
    ll ans = 0;
    for (; r >= 0; r = (r & (r + 1)) - 1) {
      ans += tree[r];
    }
    return ans;
  }
  ll get(ll l, ll r) {
    chkmax(l, 0);
    chkmin(r, n - 1);
    if (l > r) return 0;
    return get(r) - get(l - 1);
  }
};
struct Node {
  ll modSum;
  ll modAdd;
  ll sum;
  Node() : modSum(0), modAdd(0), sum(0) {}
  Node getVal(ll sz) const {
    Node ans;
    ans.sum = sum + modSum * sz + modAdd * ((ll)sz * (sz - 1) / 2);
    return ans;
  }
};
Node merge(const Node& a, const Node& b) {
  Node ans;
  ans.sum = a.sum + b.sum;
  return ans;
}
namespace SegmentTree {
Node tree[4 * N];
ll myTree[N];
void init() {}
void push(ll v, ll szL) {
  tree[v * 2].modSum += tree[v].modSum;
  tree[v * 2].modAdd += tree[v].modAdd;
  tree[v * 2 + 1].modSum += tree[v].modSum + tree[v].modAdd * szL;
  tree[v * 2 + 1].modAdd += tree[v].modAdd;
  tree[v].modSum = 0;
  tree[v].modAdd = 0;
}
ll upd(ll v, ll tl, ll tr, ll l, ll r, ll modSum) {
  if (tl >= r || tr <= l) return 0;
  if (tl >= l && tr <= r) {
    tree[v].modAdd++;
    tree[v].modSum += modSum;
    return tr - tl;
  }
  ll tm = (tl + tr) / 2;
  push(v, tm - tl);
  ll szL = upd(v * 2, tl, tm, l, r, modSum);
  szL += upd(v * 2 + 1, tm, tr, l, r, modSum + szL);
  tree[v] = merge(tree[v * 2].getVal(tm - tl), tree[v * 2 + 1].getVal(tr - tm));
  return szL;
}
void upd(ll l, ll r) {
  chkmax(l, 0);
  chkmin(r, N - 1);
  if (l > r) return;
  upd(1, 0, N, l, r + 1, 0);
}
ll get(ll v, ll tl, ll tr, ll pos) {
  if (tl >= pos + 1 || tr <= pos) return 0;
  if (tl == tr - 1) {
    return (tree[v].getVal(tr - tl)).sum;
  }
  ll tm = (tl + tr) / 2;
  push(v, tm - tl);
  ll ans = get(v * 2, tl, tm, pos) + get(v * 2 + 1, tm, tr, pos);
  tree[v] = merge(tree[v * 2].getVal(tm - tl), tree[v * 2 + 1].getVal(tr - tm));
  return ans;
}
ll get(ll pos) { return get(1, 0, N, pos); }
};  // namespace SegmentTree
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout.precision(20), cout.setf(ios::fixed);
  Fenwick sum(N);
  Fenwick cnt(N);
  SegmentTree::init();
  cin >> n;
  for (ll i = 0; i < n; ++i) {
    cin >> a[i];
  }
  ll ans = 0;
  for (ll i = 0; i < n; ++i) {
    ans += (ll)a[i] * cnt.get(a[i] + 1, N - 1);
    ans += sum.get(0, a[i] - 1);
    ans += SegmentTree::get(a[i]);
    for (ll l = a[i], step = 1; l < N; l += a[i], ++step) {
      ll r = l + a[i] - 1;
      chkmin(r, N - 1);
      ans += sum.get(l, r) - cnt.get(l, r) * a[i] * step;
    }
    cout << ans << ' ';
    cnt.upd(a[i], 1);
    sum.upd(a[i], a[i]);
    for (ll l = a[i]; l < N; l += a[i]) {
      SegmentTree::upd(l, l + a[i] - 1);
    }
  }
  cout << '\n';
  return 0;
}

```