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.File;
  import java.io.FileInputStream;
  import java.io.FileNotFoundException;
  import java.io.FileOutputStream;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.math.BigInteger;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.BitSet;
  import java.util.Calendar;
  import java.util.Collections;
  import java.util.Comparator;
  import java.util.HashMap;
  import java.util.HashSet;
  import java.util.LinkedList;
  import java.util.PriorityQueue;
  import java.util.SortedSet;
  import java.util.Stack;
  import java.util.StringTokenizer;
  import java.util.TreeMap;
  import java.util.TreeSet;
  
  /**
   * #
   *
   * @author pttrung
   */
  public class E_Round_763_Div3 {
      public static long MOD = 1000000007;
  
      static long[][] dp;
  
      public static void main(String[] args) throws FileNotFoundException {
          // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
          // "output.txt")));
          PrintWriter out = new PrintWriter(System.out);
          Scanner in = new Scanner();
          int T = in.nextInt();
          for (int Z = 0; Z < T; Z++) {
  
              int n = in.nextInt();
              int[] data = new int[n];
              TreeMap<Integer, Integer> map = new TreeMap<>();
              for (int i = 0; i < n; i++) {
                  data[i] = in.nextInt();
                  map.put(data[i], map.getOrDefault(data[i], 0) + 1);
              }
  
              Arrays.sort(data);
  
              long[] check = new long[n + 1];
              for (int i = 0; i < n; i++) {
                  if (i > 0 && check[i - 1] == -1) {
                      check[i] = -1;
                      continue;
                  }
                  check[i] = i > 0 ? check[i - 1] : 0;
                  Integer tmp = map.floorKey(i);
                  if (tmp == null) {
                      check[i] = -1;
                      continue;
                  }
                  check[i] += i - tmp;
                  map.put(tmp, map.get(tmp) - 1);
                  if (map.get(tmp) == 0) {
                      map.remove(tmp);
                  }
              }
  
              for (int i = 0; i <= n; i++) {
                  if (i > 0 && check[i - 1] == -1) {
                      out.print(-1 + " ");
                      continue;
                  }
                  int st = 0;
                  int ed = n - 1;
                  int smaller = -1;
                  while (st <= ed) {
                      int mid = (st + ed) / 2;
                      if (data[mid] < i) {
                          smaller = mid;
                          st = mid + 1;
                      } else {
                          ed = mid - 1;
                      }
                  }
                  st = 0;
                  ed = n - 1;
                  int larger = -1;
                  while (st <= ed) {
                      int mid = (st + ed) / 2;
                      if (data[mid] > i) {
                          larger = mid;
                          ed = mid - 1;
                      } else {
                          st = mid + 1;
                      }
                  }
                  long result = i > 0 ? check[i - 1] : 0;
                  int equal;
                  if (smaller != -1 && larger != -1) {
                      equal = larger - smaller - 1;
                  } else if (larger != -1) {
                      equal = larger;
                  } else if (smaller != -1) {
                      equal = n - smaller - 1;
                  } else {
                      equal = n;
                  }
  
                  result += equal;
                  out.print(result + " ");
              }
              out.println();
          }
          out.close();
      }
  
  
      static int abs(int a) {
          return a < 0 ? -a : a;
      }
  
  
      public static int[] KMP(String val) {
          int i = 0;
          int j = -1;
          int[] result = new int[val.length() + 1];
          result[0] = -1;
          while (i < val.length()) {
              while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                  j = result[j];
              }
              j++;
              i++;
              result[i] = j;
          }
          return result;
  
      }
  
      public static boolean nextPer(int[] data) {
          int i = data.length - 1;
          while (i > 0 && data[i] < data[i - 1]) {
              i--;
          }
          if (i == 0) {
              return false;
          }
          int j = data.length - 1;
          while (data[j] < data[i - 1]) {
              j--;
          }
          int temp = data[i - 1];
          data[i - 1] = data[j];
          data[j] = temp;
          Arrays.sort(data, i, data.length);
          return true;
      }
  
      public static int digit(long n) {
          int result = 0;
          while (n > 0) {
              n /= 10;
              result++;
          }
          return result;
      }
  
      public static double dist(long a, long b, long x, long y) {
          double val = (b - a) * (b - a) + (x - y) * (x - y);
          val = Math.sqrt(val);
          double other = x * x + a * a;
          other = Math.sqrt(other);
          return val + other;
  
      }
  
      public static class Point {
  
          long x;
          long y;
  
          public Point(long start, long end) {
              this.x = start;
              this.y = end;
          }
  
          public String toString() {
              return x + " " + y;
          }
  
      }
  
      public static class FT {
  
          long[] data;
  
          FT(int n) {
              data = new long[n];
          }
  
          public void update(int index, long value) {
              while (index < data.length) {
                  data[index] += value;
                  index += (index & (-index));
              }
          }
  
          public long get(int index) {
              long result = 0;
              while (index > 0) {
                  result += data[index];
                  index -= (index & (-index));
              }
              return result;
  
          }
      }
  
      public static long gcd(long a, long b) {
          if (b == 0) {
              return a;
          }
          return gcd(b, a % b);
      }
  
      public static long pow(long a, int b) {
          if (b == 0) {
              return 1;
          }
          if (b == 1) {
              return a;
          }
  
          long val = pow(a, b / 2);
          if (b % 2 == 0) {
              return val * val;
          } else {
              return val * (val * a);
  
          }
      }
  
      static class Scanner {
  
          BufferedReader br;
          StringTokenizer st;
  
          public Scanner() throws FileNotFoundException {
              // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
              br = new BufferedReader(new InputStreamReader(System.in));
              //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
          }
  
          public String next() {
  
              while (st == null || !st.hasMoreTokens()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (Exception e) {
                      throw new RuntimeException();
                  }
              }
              return st.nextToken();
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          public String nextLine() {
              st = null;
              try {
                  return br.readLine();
              } catch (Exception e) {
                  throw new RuntimeException();
              }
          }
  
          public boolean endLine() {
              try {
                  String next = br.readLine();
                  while (next != null && next.trim().isEmpty()) {
                      next = br.readLine();
                  }
                  if (next == null) {
                      return true;
                  }
                  st = new StringTokenizer(next);
                  return st.hasMoreTokens();
              } catch (Exception e) {
                  throw new RuntimeException();
              }
          }
      }
  }