CF1619E

// Problem: E. MEX and Increments
// Contest: Codeforces - Codeforces Round 762 (Div. 3)
// URL: https://codeforces.com/problemset/problem/1619/E
// Memory Limit: 256 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <assert.h>
#include <bits/stdc++.h>
using namespace std;
#ifndef __DEBUG__
#define dbg(...) 42
#endif
template <class T> using mpq = priority_queue<T, vector<T>, greater<T>>;

using ll = long long;
using a2l = array<ll, 2>;
using pll = pair<ll, ll>;
using vl = vector<ll>;

void solve()
{
    ll n, mex = 0;
    cin >> n;
    vl a(n), cnt(n + 1);
    for (auto &x : a) {
        cin >> x;
        if (x <= n)
            cnt[x] += 1;
    }
    while (mex <= n && cnt[mex])
        ++mex;

    vl ans(n + 1, -1);
    map<ll, ll> opt;
    for (ll i = 0; i < mex; ++i) {
        ans[i] = cnt[i];
        if (cnt[i] > 1)
            opt[i] = cnt[i] - 1;
    }
    ans[mex] = 0;
    for (ll i = mex + 1, acc = 0; i <= n; ++i) {
        dbg(opt);
        if (opt.size() == 0) {
            break;
        }
        auto [k, v] = *opt.rbegin();
        acc += i - 1 - k;
        if (v == 1)
            opt.erase(k);
        else
            opt[k] -= 1;
        ans[i] = acc + cnt[i];
        if (cnt[i])
            opt[i] = cnt[i];
    }
    for (auto x : ans)
        cout << x << ' ';
    cout << '\n';
}

int main(int argc, char **argv)
{
    ll t;
    cin >> t;
    while (t--)
        solve();
    return 0;
};