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: 
  // package com.company;
  
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  
  public final class Main {
  
      FastReader s;
  
      public static void main(String[] args) throws java.lang.Exception {
  
          new Main().run();
  
      }
  
      void run() {
          s = new FastReader();
          solve();
      }
  
  
  
  
      StringBuffer sb;
  
  
      void solve() {
  
          sb = new StringBuffer();
  
          for (int T = s.nextInt(); T > 0; T--)
          {
  
              start();
  
  
          }
  
  
          System.out.print(sb);
  
      }
  
  
  
      void start()
      {
  
  
           int n = s.nextInt();
           int arr[] = intArr(n);
           TreeMap<Integer,Integer> x = new TreeMap<>();
           for(int i : arr)
           {
               x.put(i,x.getOrDefault(i,0)+1);
           }
          //   sort(arr);
           TreeMap<Integer,Integer> pp = new TreeMap<>();
  
           long times = 0;
           boolean ans = false;
           for(int i = 0; i<=n; i++)
           {
               if(ans)
               {
                   sb.append("-1 ");
               }
               else if(x.containsKey(i))
               {
                   if(x.get(i) == 1)
                   {
                       sb.append((times+1)+" ");
                   }
                   else
                   {
                       int c = x.get(i);
                       sb.append((times+c)+" ");
                       c--;
                       pp.put(i,c);
                   }
               }
               else
               {
                   sb.append(times+" ");
                   Integer ll = pp.lowerKey(i);
                   if(ll == null)
                   {
                       ans = true;
                   }
                   else
                   {
                       pp.put(ll,pp.get(ll)-1);
                       if(pp.get(ll) == 0)
                           pp.remove(ll);
                       times+=(i-ll);
  
                   }
  
               }
  
           }
           sb.append("\n");
  
      }
  
  
  
  
      class Pair {
          int a;
          int b;
  
          public Pair(int a, int b) {
              this.a = a;
              this.b = b;
          }
  
          void print() {
              System.out.println(a + " " + b);
          }
  
      }
  
      class segmentTree{
           int[] tree;
           int n;
           public segmentTree(int[] nums) {
               if (nums.length > 0) {
                   n = nums.length;
                   tree = new int[n * 2];
                   buildTree(nums);
               }
           }
  
           private void buildTree(int[] nums) {
               for (int i = n, j = 0;  i < 2 * n; i++,  j++)
                   tree[i] = nums[j];
               for (int i = n - 1; i > 0; --i)
                   tree[i] = tree[i * 2] + tree[i * 2 + 1];
           }
  
           void update(int pos, int val) {
               pos += n;
               tree[pos] = val;
               while (pos > 0) {
                   int left = pos;
                   int right = pos;
                   if (pos % 2 == 0) {
                       right = pos + 1;
                   } else {
                       left = pos - 1;
                   }
                   // parent is updated after child is updated
                   tree[pos / 2] = tree[left] + tree[right];
                   pos /= 2;
               }
           }
  
           public int sumRange(int l, int r) {
               // get leaf with value 'l'
               l += n;
               // get leaf with value 'r'
               r += n;
               int sum = 0;
               while (l <= r) {
                   if ((l % 2) == 1) {
                       sum += tree[l];
                       l++;
                   }
                   if ((r % 2) == 0) {
                       sum += tree[r];
                       r--;
                   }
                   l /= 2;
                   r /= 2;
               }
               return sum;
           }
  
       }
  
      int gcd(int a, int b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      long power(long x, long y, long p) {
          long res = 1;
  
  
          x = x % p;
  
          while (y > 0) {
  
              if ((y & 1) > 0)
                  res = (res * x) % p;
  
  
              y = y >> 1;
              x = (x * x) % p;
          }
          return res;
      }
  
      int find(int dsu[], int i) {
          if (dsu[i] == i)
              return i;
          dsu[i] = find(dsu, dsu[i]);
          return dsu[i];
      }
  
      void union(int dsu[], int i, int j) {
          int a = find(dsu, i);
          int b = find(dsu, j);
          dsu[a] = b;
      }
  
      static void sort(int[] a) {
          ArrayList<Integer> l = new ArrayList<>();
          for (int i : a)
              l.add(i);
          Collections.sort(l);
          for (int i = 0; i < a.length; i++)
              a[i] = l.get(i);
      }
  
      static void sort(long[] a) {
          ArrayList<Long> l = new ArrayList<>();
          for (long i : a)
              l.add(i);
          Collections.sort(l);
          for (int i = 0; i < a.length; i++)
              a[i] = l.get(i);
      }
  
      static String sort(String s) {
          Character ch[] = new Character[s.length()];
          for (int i = 0; i < s.length(); i++) {
              ch[i] = s.charAt(i);
          }
          Arrays.sort(ch);
          StringBuffer st = new StringBuffer("");
          for (int i = 0; i < s.length(); i++) {
              st.append(ch[i]);
          }
          return st.toString();
      }
  
      // long array input
      public long[] longArr(int len) {
          // long arr input
          long[] arr = new long[len];
          String[] strs = s.nextLine().trim().split("\\s+");
          for (int i = 0; i < len; i++) {
              arr[i] = Long.parseLong(strs[i]);
  
          }
          return arr;
      }
  
      // int arr input
      public int[] intArr(int len) {
          // long arr input
          int[] arr = new int[len];
          String[] strs = s.nextLine().trim().split("\\s+");
          for (int i = 0; i < len; i++) {
              arr[i] = Integer.parseInt(strs[i]);
  
          }
          return arr;
      }
  
      public void printArray(int[] A) {
          System.out.println(Arrays.toString(A));
      }
  
      public void printArray(long[] A) {
          System.out.println(Arrays.toString(A));
      }
  
  
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              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;
          }
      }
  
  }
  