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.util.*;
  import java.io.*;
  import java.lang.*;
  
  // Problem - Multiples of 3 onn codeforces MNedium difficulty level 
  // or check on youtube channel CodeNCode
  
  public class Problem {
       static int Mod = 1000000007;
      static long dp[][];
      static int g[][];
      static int fact[];
  
  
      public static void main(String[] args) {
          MyScanner scan = new MyScanner();
          PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
           int t = scan.nextInt();
          // int t = 1;
          while (t-- > 0) {
              int n= scan.nextInt();
              long a[]= new long[n];
              
              long f[]= new long[n+1];
  
             TreeMap<Long,Long> map= new TreeMap<>();
  
              for(int i=0;i<n;i++){
                  a[i]= scan.nextLong();
                  if(map.containsKey(a[i])) map.put(a[i],map.get(a[i])+1l);
                  else map.put(a[i],1l);
                  f[(int)a[i]]++;
              }
              sort(a);
             
              long dp[]= new long[n+1];
  
               dp[0]= f[0];
  
              for(int i=1;i<=n;i++){
                  dp[i]= dp[i-1]-f[i-1] ;
                  Long x= map.floorKey((long)i-1);
                //  out.println("f"+ x);
   
                  if(x==null){
                      for(int j=i;j<=n;j++){
                          dp[j]=-1l;
                      }
                      break;
                  }
  
                  if(map.get(x)==1) map.remove(x);
                  else map.put(x,map.get(x)-1);
                  dp[i]+= (long)i-1l-(long)x;
                  dp[i]+=f[i];
              }
  
              for(int i=0;i<=n;i++){
                  out.print(dp[i]+" ");
              }
              out.println();
  
              
  
          }
  
          out.close();
      }
  
   
  
  
  
      static ArrayList<Integer> digits(long n){
          ArrayList<Integer> list= new ArrayList<>();
          while(n>0){
              list.add((int)(n%10l));
              n=n/10l;
          }
          Collections.reverse(list);
          return list;
      }
  
      static class Pair {
          int l;
          int r;
  
          Pair(int l, int r) {
              this.l = l;
              this.r = r;
          }
  
          @Override
          public int hashCode() {
              final int prime = 31;
              int result = 1;
              result = prime * result + l;
              result = prime * result + r;
              return result;
          }
  
          @Override
          public boolean equals(Object obj) {
              if (this == obj)
                  return true;
              if (obj == null)
                  return false;
              if (getClass() != obj.getClass())
                  return false;
              Pair other = (Pair) obj;
              if (l != other.l)
                  return false;
              if (r != other.r)
                  return false;
              return true;
          }
  
          @Override
          public String toString() {
              return "Pair [l=" + l + ", r=" + r + "]";
          }
  
      }
  
      public static void reverse(int a[]) {
          int n = a.length;
          for (int i = 0; i < n / 2; i++) {
              int temp = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = temp;
          }
      }
  
      public static void sort(int[] array) {
          ArrayList<Integer> copy = new ArrayList<>();
          for (Integer i : array)
              copy.add(i);
          Collections.sort(copy);
          for (int i = 0; i < array.length; i++)
              array[i] = copy.get(i);
      }
  
      public static void sort(long[] array) {
          ArrayList<Long> copy = new ArrayList<>();
          for (Long i : array)
              copy.add(i);
          Collections.sort(copy);
          for (int i = 0; i < array.length; i++)
              array[i] = copy.get(i);
      }
  
      public static long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b); // gcd(a,b) = gcd(a-b,b) or gcd(a,b) = gcd(b,a%b) where a>b
      }
  
      public static int gcd(int a, int b) {
          if (b == 0)
              return a;
          return gcd(b, a % b); // gcd(a,b) = gcd(a-b,b) or gcd(a,b) = gcd(b,a%b) where a>b
      }
  
      public static long lcm(long a, long b) {
          return (a / gcd(a, b)) * b;
      }
  
      static long power(long x, long y) {
          long temp;
          if (y == 0) // a^b= (a^b/2)^2 if b is even
              return 1; // = (a*a^(b-1)) if b is odd
          temp = power(x, y / 2);
          if (y % 2 == 0)
              return temp * temp;
          else
              return x * temp * temp;
      }
  
      static long mod(long x) {
          return ((x % Mod + Mod) % Mod);
      }
  
      static long add(long a, long b) {
          return mod(mod(a) + mod(b));
      }
  
      static int mod(int x) {
          return ((x % Mod + Mod) % Mod);
      }
  
      static int add(int a, int b) {
          return mod(mod(a) + mod(b));
      }
  
      static int sub(int a, int b) {
          return mod(mod(a) - mod(b) + Mod);
      }
  
      static long mul(long a, long b) {
          return mod(mod(a) * mod(b));
      }
  
      static long pow(long x, long y, long p) {
          long res = 1; // Initialize result
          x = x % p; // Update x if it is more than or equal to p
  
          if (x == 0)
              return 0; // In case x is divisible by p;
  
          while (y > 0) {
              // If y is odd, multiply x with result
              if ((y & 1) != 0)
                  res = (res * x) % p;
  
              // y must be even now
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res;
      }
  
      static long modInverse(long a, long m) {
          // int g = gcd(a, m);
          // if (g != 1)
          // System.out.println("Inverse doesn't exist");
          // else {
          // // If a and m are relatively prime, then modulo
          // // inverse is a^(m-2) mode m
          // return power(a, m - 2, m);
          // }
          return pow(a, m - 2, m);
      }
  
  }
  
  class MyScanner {
      BufferedReader br;
      StringTokenizer st;
  
      public MyScanner() {
          br = new BufferedReader(new InputStreamReader(System.in));
      }
  
      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;
      }
  
  }
  