#include <bits/stdc++.h>  // {{{

#include <version>
#ifdef __cpp_lib_ranges_enumerate
#include <ranges>
namespace rv = std::views;
namespace rs = std::ranges;
#endif

// https://codeforces.com/blog/entry/96344

#pragma GCC optimize("O2,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

using namespace std;

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f64 = double;
using f128 = long double;

#if __cplusplus >= 202002L
template <typename T>
constexpr T MIN = std::numeric_limits<T>::min();

template <typename T>
constexpr T MAX = std::numeric_limits<T>::max();

template <typename T>
[[nodiscard]] static T sc(auto&& x) {
  return static_cast<T>(x);
}

template <typename T>
[[nodiscard]] static T sz(auto&& x) {
  return static_cast<T>(x.size());
}
#endif

static void NO() {
  std::cout << "NO\n";
}

static void YES() {
  std::cout << "YES\n";
}

template <typename T>
using vec = std::vector<T>;

#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define ff first
#define ss second

#ifdef LOCAL
#define db(...) std::print(__VA_ARGS__)
#define dbln(...) std::println(__VA_ARGS__)
#else
#define db(...)
#define dbln(...)
#endif
//  }}}

void solve() {
  u32 n;
  cin >> n;

  vec<u64> a(n);
  for (auto& e : a)
    cin >> e;
  map<u32, u64> f;
  for (auto e : a)
    ++f[e];

  u64 pull = 0;
  vec<i64> ans(n + 1, -1);
  vec<u32> available;

  for (u32 mex = 0; mex <= n; ++mex) {
    if (mex > 0 && f[mex - 1] == 0) {
      if (available.empty()) {
        break;
      }
      pull += mex - 1 - available.back();
      available.pop_back();
    }
    ans[mex] = pull + f[mex];

    for (u32 i = 0; i < (f[mex] > 0 ? f[mex] - 1 : 0); ++i) {
      available.push_back(mex);
    }
  }

  for (u32 i = 0; i <= n; ++i) {
    cout << ans[i] << " \n"[i == n];
  }
}

int main() {  // {{{
  std::cin.exceptions(std::cin.failbit);

#ifdef LOCAL
  std::cerr.rdbuf(std::cout.rdbuf());
  std::cout.setf(std::ios::unitbuf);
  std::cerr.setf(std::ios::unitbuf);
#else
  std::cin.tie(nullptr)->sync_with_stdio(false);
#endif

  u32 tc = 1;
  std::cin >> tc;

  for (u32 t = 0; t < tc; ++t) {
    solve();
  }

  return 0;
}
// }}}