description: 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. 
solution: import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.PrintStream;
  import java.io.File;
  import java.io.FileInputStream;
  import java.util.*;
  
  public class Main {
  
      // static final File ip = new File("input.txt");
      // static final File op = new File("output.txt");
      // static {
      //     try {
      //         System.setOut(new PrintStream(op));
      //         System.setIn(new FileInputStream(ip));
      //     } catch (Exception e) {
      //     }
      // }
  
      public static void main(String[] args) {
          FastReader sc = new FastReader();
          // int test = 1;
          int test = sc.nextInt();
          while (test-- > 0) {
              int n = sc.nextInt();
              int[] arr = new int[n];
              TreeSet<Integer> tree = new TreeSet<>();
              for (int i = 0; i < n; i++) {
                  arr[i] = sc.nextInt();
                  tree.add(arr[i]);
              }
              int[] count = new int[n + 1];
              for (int e : arr)
                  count[e]++;
  
              long[] ans = new long[n + 1];
              Arrays.fill(ans, -1);
              long mex = 0;
              for (int i = 0; i <= n; i++) {
                  // mex;
                  ans[i] = mex + count[i];
  
                  // set the ele
                  if (tree.floor(i) == null)
                      break;
                  int ele = tree.floor(i);
                  count[ele]--;
                  if (count[ele] == 0)
                      tree.remove(ele);
                  mex += i - ele;
              }
              for (long e : ans) {
                  System.out.print(e + " ");
              }
              System.out.println();
          }
      }
  
      static long power(long x, long y, long p) {
          long res = 1;
          x = x % p;
          if (x == 0)
              return 0;
          while (y > 0) {
              if ((y & 1) != 0)
                  res = (res * x) % p;
              y = y >> 1;
              x = (x * x) % p;
          }
          return res;
      }
  
      public static int countSetBits(long number) {
          int count = 0;
          while (number > 0) {
              ++count;
              number &= number - 1;
          }
          return count;
      }
  
      static int lower_bound(long target, long[] a, int pos) {
          if (pos >= a.length)
              return -1;
          int low = pos, high = a.length - 1;
          while (low < high) {
              int mid = low + (high - low) / 2;
              if (a[mid] < target)
                  low = mid + 1;
              else
                  high = mid;
          }
          return a[low] >= target ? low : -1;
      }
  
      private static <T> void swap(long[] a, int i, int j) {
          long tmp = a[i];
          a[i] = a[j];
          a[j] = tmp;
      }
  
      static class pair {
          long a;
          int b;
  
          pair(long x, int y) {
              this.a = x;
              this.b = y;
          }
      }
  
      static class first implements Comparator<pair> {
  
          public int compare(pair p1, pair p2) {
              if (p1.a > p2.a)
                  return 1;
              else if (p1.a < p2.a)
                  return -1;
              return 0;
          }
      }
  
      static class second implements Comparator<pair> {
  
          public int compare(pair p1, pair p2) {
              if (p1.b > p2.b)
                  return 1;
              else if (p1.b < p2.b)
                  return -1;
              return 0;
          }
      }
  
      private static long getSum(int[] array) {
          long sum = 0;
          for (int value : array) {
              sum += value;
          }
          return sum;
      }
  
      private static boolean isPrime(Long x) {
          if (x < 2)
              return false;
          for (long d = 2; d * d <= x; ++d) {
              if (x % d == 0)
                  return false;
          }
          return true;
      }
  
      static int[] reverse(int a[]) {
          int n = a.length;
          int i, k;
          int t;
          for (i = 0; i < n / 2; i++) {
              t = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = t;
          }
          return a;
      }
  
      private static boolean isPrimeInt(int x) {
          if (x < 2)
              return false;
          for (int d = 2; d * d <= x; ++d) {
              if (x % d == 0)
                  return false;
          }
          return true;
      }
  
      public static String reverse(String input) {
          StringBuilder str = new StringBuilder("");
  
          for (int i = input.length() - 1; i >= 0; i--) {
              str.append(input.charAt(i));
          }
  
          return str.toString();
      }
  
      private static int[] getPrimes(int n) {
          boolean[] used = new boolean[n + 1];
          used[0] = used[1] = true;
          // int size = 0;
          for (int i = 2; i <= n; ++i) {
              if (!used[i]) {
                  // ++size;
                  for (int j = 2 * i; j <= n; j += i) {
                      used[j] = true;
                  }
              }
          }
          int[] primes = new int[n + 1];
          for (int i = 0; i <= n; ++i) {
              if (!used[i]) {
                  primes[i] = 1;
              }
          }
          return primes;
      }
  
      private static long lcm(long a, long b) {
          return a / gcd(a, b) * b;
      }
  
      private static long gcd(long a, long b) {
          return (a == 0 ? b : gcd(b % a, a));
      }
  
      static void sortI(int[] arr) {
          int n = arr.length;
          Random rnd = new Random();
          for (int i = 0; i < n; ++i) {
              int tmp = arr[i];
              int randomPos = i + rnd.nextInt(n - i);
              arr[i] = arr[randomPos];
              arr[randomPos] = tmp;
          }
          Arrays.sort(arr);
      }
  
      static void shuffleList(ArrayList<Long> arr) {
          int n = arr.size();
          Random rnd = new Random();
          for (int i = 0; i < n; ++i) {
              long tmp = arr.get(i);
              int randomPos = i + rnd.nextInt(n - i);
              arr.set(i, arr.get(randomPos));
              arr.set(randomPos, tmp);
          }
      }
  
      static void factorize(long n) {
          int count = 0;
          while (!(n % 2 > 0)) {
              n >>= 1;
  
              count++;
          }
          if (count > 0) {
              // System.out.println("2" + " " + count);
          }
          long i = 0;
          for (i = 3; i <= (long) Math.sqrt(n); i += 2) {
              count = 0;
              while (n % i == 0) {
                  count++;
                  n = n / i;
              }
              if (count > 0) {
                  // System.out.println(i + " " + count);
              }
          }
  
          if (n > 2) {
              // System.out.println(i + " " + count);
          }
      }
  
      static void sortL(long[] arr) {
          int n = arr.length;
          Random rnd = new Random();
          for (int i = 0; i < n; ++i) {
              long tmp = arr[i];
              int randomPos = i + rnd.nextInt(n - i);
              arr[i] = arr[randomPos];
              arr[randomPos] = tmp;
          }
          Arrays.sort(arr);
      }
  
      ////////////////////////////////// DSU START ///////////////////////////
  
      static class DSU {
          int[] parent, rank, total_Elements;
  
          DSU(int n) {
              parent = new int[n + 1];
              rank = new int[n + 1];
              total_Elements = new int[n + 1];
              for (int i = 0; i <= n; i++) {
                  parent[i] = i;
                  rank[i] = 1;
                  total_Elements[i] = 1;
              }
          }
  
          int find(int u) {
              if (parent[u] == u)
                  return u;
              return parent[u] = find(parent[u]);
          }
  
          void unionByRank(int u, int v) {
              int pu = find(u);
              int pv = find(v);
  
              if (pu != pv) {
                  if (rank[pu] > rank[pv]) {
                      parent[pv] = pu;
                      total_Elements[pu] += total_Elements[pv];
                  } else if (rank[pu] < rank[pv]) {
                      parent[pu] = pv;
                      total_Elements[pv] += total_Elements[pu];
                  } else {
                      parent[pu] = pv;
                      total_Elements[pv] += total_Elements[pu];
                      rank[pv]++;
                  }
              }
          }
  
          boolean unionBySize(int u, int v) {
              u = find(u);
              v = find(v);
              if (u != v) {
                  parent[u] = v;
                  total_Elements[v] += total_Elements[u];
                  total_Elements[u] = 0;
                  return true;
              }
              return false;
          }
      }
  
      ////////////////////////////////// DSU END /////////////////////////////
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          public boolean hasNext() {
              return false;
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
          double nextDouble() {
              return Double.parseDouble(next());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
  }