#include <bits/stdc++.h>
using namespace std;
using namespace chrono;
const long long INF = (long long)2e18;
const long long one = (long long)1e5 + 1;
const long double PI = 3.141592653589793238462;
long long mod = (long long)1000000007;
long long mod2 = (long long)998244353;
long long expo(long long a, long long b, long long mod) {
  long long res = 1ll;
  while (b > 0) {
    if (b & 1ll) res = (res * a) % mod;
    a = (a * a) % mod;
    b = b >> 1ll;
  }
  return res;
}
void extendgcd(long long a, long long b, long long* v) {
  if (b == 0) {
    v[0] = 1;
    v[1] = 0;
    v[2] = a;
    return;
  }
  extendgcd(b, a % b, v);
  long long x = v[1];
  v[1] = v[0] - v[1] * (a / b);
  v[0] = x;
  return;
}
long long mminv(long long a, long long b) {
  long long arr[3];
  extendgcd(a, b, arr);
  return arr[0];
}
long long mminvprime(long long a, long long b) { return expo(a, b - 2, b); }
bool revsort(long long a, long long b) { return a > b; }
void swap(int& x, int& y) {
  int temp = x;
  x = y;
  y = temp;
}
long long combination(long long n, long long r, long long m, long long* fact,
                      long long* ifact) {
  long long val1 = fact[n];
  long long val2 = ifact[n - r];
  long long val3 = ifact[r];
  return (((val1 * val2) % m) * val3) % m;
}
void google(int t) { cout << "Case #" << t << ": "; }
vector<long long> sieve(int n) {
  int* arr = new int[n + 1]();
  vector<long long> vect;
  for (int i = 2; i <= n; i++)
    if (arr[i] == 0) {
      vect.push_back(i);
      for (int j = 2 * i; j <= n; j += i) arr[j] = 1;
    }
  return vect;
}
long long mod_add(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a + b) % m) + m) % m;
}
long long mod_mul(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a * b) % m) + m) % m;
}
long long mod_sub(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a - b) % m) + m) % m;
}
long long mod_div(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (mod_mul(a, mminvprime(b, m), m) + m) % m;
}
long long phin(long long n) {
  long long number = n;
  if (n % 2 == 0) {
    number /= 2;
    while (n % 2 == 0) n /= 2;
  }
  for (long long i = 3; i <= sqrt(n); i += 2) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      number = (number / i * (i - 1));
    }
  }
  if (n > 1) number = (number / n * (n - 1));
  return number;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6) {
    if (n % i == 0 || n % (i + 2) == 0) {
      return false;
    }
  }
  return true;
}
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <typename T>
void sort(vector<T>& v) {
  sort(v.begin(), v.end());
  return;
}
template <typename T>
void sortbig(vector<T>& v) {
  sort(v.begin(), v.end(), greater<T>());
  return;
}
template <typename T>
ostream& operator<<(ostream& stream, vector<T>& v) {
  for (T& x : v) stream << x << " ";
  return stream;
}
template <typename T>
istream& operator>>(istream& stream, vector<T>& v) {
  for (T& x : v) stream >> x;
  return stream;
}
struct Node {
  long long index;
  long long value;
  Node(long long index, long long value) : index(index), value(value) {}
};
struct Edge {
  int to;
  long long cost;
  Edge(int to, long long cost) : to(to), cost(cost) {}
};
bool sortbysec(const pair<long long, long long>& a,
               const pair<long long, long long>& b) {
  return (a.second < b.second);
}
struct CompareNode {
  bool operator()(Node const& p1, Node const& p2) {
    return p1.value > p2.value;
  }
};
struct ComparePair {
  bool operator()(pair<long long, long long> const& p1,
                  pair<long long, long long> const& p2) {
    return p1.second < p2.second;
  }
};
bool sortcolbig(const vector<long long>& v1, const vector<long long>& v2) {
  return v1[0] > v2[0];
}
bool sortcol(const vector<long long>& v1, const vector<long long>& v2) {
  return v1[1] < v2[1];
}
long long x_max = (long long)5e5 + 1;
void solve(int test) {
  long long n;
  cin >> n;
  vector<long long> arr(n);
  cin >> arr;
  vector<bool> brr(n, 0);
  set<long long> use;
  vector<long long> count(n + 1, 0ll);
  for (long long i = (0); i < long long(long long(n)); ++i) {
    use.insert(arr[i]);
    count[arr[i]]++;
  }
  vector<long long> steps(n + 1, 0ll);
  priority_queue<pair<long long, long long> > second;
  if (count[0] > 1) second.push({0, count[0] - 1});
  if (count[0] == 0) {
    steps[0] = -1;
  }
  for (long long i = (1); i < long long(n + 1); ++i) {
    if (steps[i - 1] == -1) {
      steps[i] = -1;
      continue;
    }
    if (count[i] == 1) {
      steps[i] = steps[i - 1];
      continue;
    }
    if (count[i] > 1) {
      steps[i] = steps[i - 1];
      second.push({i, count[i] - 1});
    } else {
      if ((int)(second.size()) > 0) {
        pair<long long, long long> temp = second.top();
        second.pop();
        steps[i] = i - temp.first + steps[i - 1];
        --temp.second;
        if (temp.second > 0) {
          second.push(temp);
        }
      } else {
        steps[i] = -1;
      }
    }
  }
  for (long long i = (0); i < long long(long long(n + 1)); ++i) {
    if (i == 0) {
      cout << count[0] << " ";
      continue;
    } else {
      if (steps[i - 1] == -1) {
        cout << -1 << " ";
      } else {
        cout << steps[i - 1] + count[i] << " ";
      }
    }
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  int tp = 1;
  cin >> t;
  while (t--) {
    auto src = high_resolution_clock::now();
    solve(tp);
    auto stop = high_resolution_clock::now();
    auto duration = duration_cast<microseconds>(stop - src);
    tp++;
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Dmitry has an array of n non-negative integers a_1, a_2, ..., a_n.

In one operation, Dmitry can choose any index j (1 ≤ j ≤ n) and increase the value of the element a_j by 1. He can choose the same index j multiple times.

For each i from 0 to n, determine whether Dmitry can make the MEX of the array equal to exactly i. If it is possible, then determine the minimum number of operations to do it.

The MEX of the array is equal to the minimum non-negative integer that is not in the array. For example, the MEX of the array [3, 1, 0] is equal to 2, and the array [3, 3, 1, 4] is equal to 0.

Input

The first line of input data contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. 

The descriptions of the test cases follow.

The first line of the description of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line of the description of each test case contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ n) — elements of the array a.

It is guaranteed that the sum of the values n over all test cases in the test does not exceed 2⋅10^5.

Output

For each test case, output n + 1 integer — i-th number is equal to the minimum number of operations for which you can make the array MEX equal to i (0 ≤ i ≤ n), or -1 if this cannot be done.

Example

Input


5
3
0 1 3
7
0 1 2 3 4 3 2
4
3 0 0 0
7
4 6 2 3 5 0 5
5
4 0 1 0 4


Output


1 1 0 -1 
1 1 2 2 1 0 2 6 
3 0 1 4 3 
1 0 -1 -1 -1 -1 -1 -1 
2 1 0 2 -1 -1 

Note

In the first set of example inputs, n=3:

  * to get MEX=0, it is enough to perform one increment: a_1++; 
  * to get MEX=1, it is enough to perform one increment: a_2++; 
  * MEX=2 for a given array, so there is no need to perform increments; 
  * it is impossible to get MEX=3 by performing increments. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using namespace chrono;
const long long INF = (long long)2e18;
const long long one = (long long)1e5 + 1;
const long double PI = 3.141592653589793238462;
long long mod = (long long)1000000007;
long long mod2 = (long long)998244353;
long long expo(long long a, long long b, long long mod) {
  long long res = 1ll;
  while (b > 0) {
    if (b & 1ll) res = (res * a) % mod;
    a = (a * a) % mod;
    b = b >> 1ll;
  }
  return res;
}
void extendgcd(long long a, long long b, long long* v) {
  if (b == 0) {
    v[0] = 1;
    v[1] = 0;
    v[2] = a;
    return;
  }
  extendgcd(b, a % b, v);
  long long x = v[1];
  v[1] = v[0] - v[1] * (a / b);
  v[0] = x;
  return;
}
long long mminv(long long a, long long b) {
  long long arr[3];
  extendgcd(a, b, arr);
  return arr[0];
}
long long mminvprime(long long a, long long b) { return expo(a, b - 2, b); }
bool revsort(long long a, long long b) { return a > b; }
void swap(int& x, int& y) {
  int temp = x;
  x = y;
  y = temp;
}
long long combination(long long n, long long r, long long m, long long* fact,
                      long long* ifact) {
  long long val1 = fact[n];
  long long val2 = ifact[n - r];
  long long val3 = ifact[r];
  return (((val1 * val2) % m) * val3) % m;
}
void google(int t) { cout << "Case #" << t << ": "; }
vector<long long> sieve(int n) {
  int* arr = new int[n + 1]();
  vector<long long> vect;
  for (int i = 2; i <= n; i++)
    if (arr[i] == 0) {
      vect.push_back(i);
      for (int j = 2 * i; j <= n; j += i) arr[j] = 1;
    }
  return vect;
}
long long mod_add(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a + b) % m) + m) % m;
}
long long mod_mul(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a * b) % m) + m) % m;
}
long long mod_sub(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a - b) % m) + m) % m;
}
long long mod_div(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (mod_mul(a, mminvprime(b, m), m) + m) % m;
}
long long phin(long long n) {
  long long number = n;
  if (n % 2 == 0) {
    number /= 2;
    while (n % 2 == 0) n /= 2;
  }
  for (long long i = 3; i <= sqrt(n); i += 2) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      number = (number / i * (i - 1));
    }
  }
  if (n > 1) number = (number / n * (n - 1));
  return number;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6) {
    if (n % i == 0 || n % (i + 2) == 0) {
      return false;
    }
  }
  return true;
}
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <typename T>
void sort(vector<T>& v) {
  sort(v.begin(), v.end());
  return;
}
template <typename T>
void sortbig(vector<T>& v) {
  sort(v.begin(), v.end(), greater<T>());
  return;
}
template <typename T>
ostream& operator<<(ostream& stream, vector<T>& v) {
  for (T& x : v) stream << x << " ";
  return stream;
}
template <typename T>
istream& operator>>(istream& stream, vector<T>& v) {
  for (T& x : v) stream >> x;
  return stream;
}
struct Node {
  long long index;
  long long value;
  Node(long long index, long long value) : index(index), value(value) {}
};
struct Edge {
  int to;
  long long cost;
  Edge(int to, long long cost) : to(to), cost(cost) {}
};
bool sortbysec(const pair<long long, long long>& a,
               const pair<long long, long long>& b) {
  return (a.second < b.second);
}
struct CompareNode {
  bool operator()(Node const& p1, Node const& p2) {
    return p1.value > p2.value;
  }
};
struct ComparePair {
  bool operator()(pair<long long, long long> const& p1,
                  pair<long long, long long> const& p2) {
    return p1.second < p2.second;
  }
};
bool sortcolbig(const vector<long long>& v1, const vector<long long>& v2) {
  return v1[0] > v2[0];
}
bool sortcol(const vector<long long>& v1, const vector<long long>& v2) {
  return v1[1] < v2[1];
}
long long x_max = (long long)5e5 + 1;
void solve(int test) {
  long long n;
  cin >> n;
  vector<long long> arr(n);
  cin >> arr;
  vector<bool> brr(n, 0);
  set<long long> use;
  vector<long long> count(n + 1, 0ll);
  for (long long i = (0); i < long long(long long(n)); ++i) {
    use.insert(arr[i]);
    count[arr[i]]++;
  }
  vector<long long> steps(n + 1, 0ll);
  priority_queue<pair<long long, long long> > second;
  if (count[0] > 1) second.push({0, count[0] - 1});
  if (count[0] == 0) {
    steps[0] = -1;
  }
  for (long long i = (1); i < long long(n + 1); ++i) {
    if (steps[i - 1] == -1) {
      steps[i] = -1;
      continue;
    }
    if (count[i] == 1) {
      steps[i] = steps[i - 1];
      continue;
    }
    if (count[i] > 1) {
      steps[i] = steps[i - 1];
      second.push({i, count[i] - 1});
    } else {
      if ((int)(second.size()) > 0) {
        pair<long long, long long> temp = second.top();
        second.pop();
        steps[i] = i - temp.first + steps[i - 1];
        --temp.second;
        if (temp.second > 0) {
          second.push(temp);
        }
      } else {
        steps[i] = -1;
      }
    }
  }
  for (long long i = (0); i < long long(long long(n + 1)); ++i) {
    if (i == 0) {
      cout << count[0] << " ";
      continue;
    } else {
      if (steps[i - 1] == -1) {
        cout << -1 << " ";
      } else {
        cout << steps[i - 1] + count[i] << " ";
      }
    }
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  int tp = 1;
  cin >> t;
  while (t--) {
    auto src = high_resolution_clock::now();
    solve(tp);
    auto stop = high_resolution_clock::now();
    auto duration = duration_cast<microseconds>(stop - src);
    tp++;
  }
  return 0;
}

```