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.lang.*;
  import java.rmi.ConnectIOException;
  import java.io.*;
  
  public class Main {
      static FastReader in;
      static PrintWriter out;
  
      static int bit(long n) {
          return (n == 0) ? 0 : (1 + bit(n & (n - 1)));
      }
  
      static void p(Object o) {
          out.print(o);
      }
  
      static void pn(Object o) {
          out.println(o);
      }
  
      static void pni(Object o) {
          out.println(o);
          out.flush();
      }
  
      static String n() throws Exception {
          return in.next();
      }
  
      static String nln() throws Exception {
          return in.nextLine();
      }
  
      static int ni() throws Exception {
          return Integer.parseInt(in.next());
      }
  
      static long nl() throws Exception {
          return Long.parseLong(in.next());
      }
  
      static double nd() throws Exception {
          return Double.parseDouble(in.next());
      }
  
      static class FastReader {
          static BufferedReader br;
          static StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          public FastReader(String s) throws Exception {
              br = new BufferedReader(new FileReader(s));
          }
  
          String next() throws Exception {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      throw new Exception(e.toString());
                  }
              }
              return st.nextToken();
          }
  
          String nextLine() throws Exception {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  throw new Exception(e.toString());
              }
              return str;
          }
      }
  
      static long power(long a, long b) {
          if (b == 0)
              return 1;
          long val = power(a, b / 2);
          val = val * val;
          if ((b % 2) != 0)
              val = val * a;
          return val;
      }
  
      static long power(long a, long b, long mod) {
          if (b == 0)
              return 1L;
          long val = power(a, b / 2) % mod;
          val = (val * val) % mod;
          if ((b % 2) != 0)
              val = (val * a) % mod;
          return val % mod;
      }
  
      static ArrayList<Long> prime_factors(long n) {
          ArrayList<Long> ans = new ArrayList<Long>();
          while (n % 2 == 0) {
              ans.add(2L);
              n /= 2L;
          }
          for (long i = 3; i <= Math.sqrt(n); i++) {
              while (n % i == 0) {
                  ans.add(i);
                  n /= i;
              }
          }
          if (n > 2) {
              ans.add(n);
          }
          return ans;
      }
  
      static void sort(ArrayList<Long> a) {
          Collections.sort(a);
      }
  
      static void reverse_sort(ArrayList<Long> a) {
          Collections.sort(a, Collections.reverseOrder());
      }
  
      static void swap(long[] a, int i, int j) {
          long temp = a[i];
          a[i] = a[j];
          a[j] = temp;
      }
  
      static void swap(List<Long> a, int i, int j) {
          long temp = a.get(i);
          a.set(j, a.get(i));
          a.set(j, temp);
      }
  
      static void sieve(boolean[] prime) {
          int n = prime.length - 1;
          Arrays.fill(prime, true);
          for (int i = 2; i * i <= n; i++) {
              if (prime[i]) {
                  for (int j = 2 * i; j <= n; j += i) {
                      prime[j] = false;
                  }
              }
          }
      }
  
      static long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      static long mod = 1000000007;
  
      public static void sort(long[] arr, int l, int r) {
          if (l >= r)
              return;
          int mid = (l + r) / 2;
          sort(arr, l, mid);
          sort(arr, mid + 1, r);
          merge(arr, l, mid, r);
      }
  
      public static void sort(int[] arr, int l, int r) {
          if (l >= r)
              return;
          int mid = (l + r) / 2;
          sort(arr, l, mid);
          sort(arr, mid + 1, r);
          merge(arr, l, mid, r);
      }
  
      static void merge(int[] arr, int l, int mid, int r) {
          int[] left = new int[mid - l + 1];
          int[] right = new int[r - mid];
          for (int i = l; i <= mid; i++) {
              left[i - l] = arr[i];
          }
          for (int i = mid + 1; i <= r; i++) {
              right[i - (mid + 1)] = arr[i];
          }
          int left_start = 0;
          int right_start = 0;
          int left_length = mid - l + 1;
          int right_length = r - mid;
          int temp = l;
          while (left_start < left_length && right_start < right_length) {
              if (left[left_start] < right[right_start]) {
                  arr[temp] = left[left_start++];
              } else {
                  arr[temp] = right[right_start++];
              }
              temp++;
          }
          while (left_start < left_length) {
              arr[temp++] = left[left_start++];
          }
          while (right_start < right_length) {
              arr[temp++] = right[right_start++];
          }
      }
  
      static void merge(long[] arr, int l, int mid, int r) {
          long[] left = new long[mid - l + 1];
          long[] right = new long[r - mid];
          for (int i = l; i <= mid; i++) {
              left[i - l] = arr[i];
          }
          for (int i = mid + 1; i <= r; i++) {
              right[i - (mid + 1)] = arr[i];
          }
          int left_start = 0;
          int right_start = 0;
          int left_length = mid - l + 1;
          int right_length = r - mid;
          int temp = l;
          while (left_start < left_length && right_start < right_length) {
              if (left[left_start] < right[right_start]) {
                  arr[temp] = left[left_start++];
              } else {
                  arr[temp] = right[right_start++];
              }
              temp++;
          }
          while (left_start < left_length) {
              arr[temp++] = left[left_start++];
          }
          while (right_start < right_length) {
              arr[temp++] = right[right_start++];
          }
      }
  
      static class pair implements Comparable<pair> {
          int a, b;
  
          public pair(int a, int b) {
              this.a = a;
              this.b = b;
          }
  
          public int compareTo(pair p) {
              if (this.a == p.a)
                  return this.b - p.b;
              return this.a - p.a;
          }
  
      }
  
      static HashMap<Long, Integer> map_prime_factors(long n) {
          HashMap<Long, Integer> map = new HashMap<>();
          while (n % 2 == 0) {
              map.put(2L, map.getOrDefault(2L, 0) + 1);
              n /= 2L;
          }
          for (long i = 3; i <= Math.sqrt(n); i++) {
              while (n % i == 0) {
                  map.put(i, map.getOrDefault(i, 0) + 1);
                  n /= i;
              }
          }
          if (n > 2) {
              map.put(n, map.getOrDefault(n, 0) + 1);
          }
          return map;
      }
  
      static int count = 1;
      static int[] p = new int[100002];
      static long[] flat_tree = new long[300002];
      static int[] in_time = new int[1000002];
      static int[] out_time = new int[1000002];
      static long[] subtree_gcd = new long[100002];
      static int w = 0;
      static boolean poss = true;
  
      public static void main(String[] args) throws Exception {
          in = new FastReader();
          out = new PrintWriter(System.out);
          int t = ni();
          while (t-- > 0) {
              int n = ni();
              Map<Integer, Integer> map = new HashMap<>();
              TreeSet<Integer> set = new TreeSet<>();
              int[] a = new int[n];
              for (int i = 0; i < n; i++) {
                  a[i] = ni();
                  map.put(a[i], map.getOrDefault(a[i], 0) + 1);
              }
              int mex = -1;
              for (int i = 0; i <= n; i++) {
                  if (!map.containsKey(i)) {
                      mex = i;
                      break;
                  }
              }
              sort(a, 0, n - 1);
              TreeMap<Integer, Integer> extra = new TreeMap<>();
              long[] ans = new long[n + 1];
              int last = -1;
              for (int i = 0; i < mex; i++) {
                  ans[i] = map.get(i);
                  if (map.get(i) == 1)
                      continue;
                  else {
                      extra.put(i, map.get(i) - 1);
                  }
              }
              ans[mex] = 0;
              // if (extra.size() == 0) {
              //     for (int i = mex + 1; i <= n; i++)
              //         ans[i] = -1;
              //     for (int i = 0; i <= n; i++)
              //         p(ans[i] + " ");
              //     pn("");
              //     continue;
              // } else {
              //     last = extra.lastKey();
              //     ans[mex]=mex-last;
              //     if (extra.get(last) == 1)
              //         extra.remove(last);
              //     else
              //         extra.put(last, extra.get(last) - 1);
              // }
              for (int i = mex + 1; i <= n; i++) {
                  if (ans[i - 1] == -1) {
                      ans[i] = -1;
                      continue;
                  }
                  if (map.containsKey(i-1)) {
                      ans[i] = ans[i - 1] +(long)map.getOrDefault(i, 0);
                  } else {
                      if (extra.size() == 0)
                          ans[i] = -1;
                      else {
                          last = extra.lastKey();
                          ans[i] = ans[i - 1] + (long)((i-1) - last+map.getOrDefault(i, 0));
                          if (extra.get(last) == 1)
                              extra.remove(last);
                          else
                              extra.put(last, extra.get(last) - 1);
                      }
                  }
                  if (map.containsKey(i) && map.get(i) > 1) {
                      extra.put(i, map.get(i) - 1);
                      last = i;
                  }
                  ans[i]-=(long)map.getOrDefault(i-1,0);
              }
              for (int i = 0; i <= n; i++) {
                  if(i==mex)p("0 ");
                  else p(ans[i] + " ");
              }
              pn("");
          }
          out.flush();
          out.close();
      }
  
      static void find(int l, int r, int level, int[] arr, int[] depth) {
          if (r < l)
              return;
          int max = find(l, r, arr);
          depth[max] = level;
          find(l, max - 1, level + 1, arr, depth);
          find(max + 1, r, level + 1, arr, depth);
      }
  
      static int find(int l, int r, int[] arr) {
          int index = l;
          for (int i = l + 1; i <= r; i++) {
              if (arr[index] < arr[i]) {
                  index = i;
              }
          }
          return index;
      }
  
      static long start(int[] a, int k) {
          if (a.length == 0)
              return 0;
          if (a.length <= k)
              return 2 * a[a.length - 1];
          long ans = 0;
          int i = 0;
          for (i = k - 1; i < a.length; i += k) {
              ans += 2 * a[i];
          }
          i -= k;
          if (i != a.length - 1) {
              return ans + 2 * a[a.length - 1];
          } else
              return ans;
      }
  
      static long end(int[] a, int k) {
          if (a.length == 0)
              return 0;
          if (a.length <= k)
              return a[a.length - 1];
          if (k == 1) {
              long sum = 0;
              for (int i = 0; i < a.length - 1; i++)
                  sum += 2 * a[i];
              return sum + a[a.length - 1];
          }
          long ans = 0;
          int i = 0;
          for (i = k - 1; i < a.length; i += k) {
              if (i != a.length - 1)
                  ans += 2 * a[i];
          }
          i -= k;
          return ans + a[a.length - 1];
      }
  
      static void print(int[] a) {
          for (int i = 0; i < a.length; i++)
              p(a[i] + " ");
          pn("");
      }
  
      static long count(long n) {
          long count = 0;
          while (n != 0) {
              n /= 10;
              count++;
          }
          return count;
      }
  
      static void swap(long a, long b) {
          long temp = a;
          a = b;
          b = temp;
      }
  
      static void swap(int[] a, int i, int j) {
          int temp = a[i];
          a[i] = a[j];
          a[j] = temp;
      }
  
      static int LcsOfPrefix(String a, String b) {
          int i = 0;
          int j = 0;
          int count = 0;
          while (i < a.length() && j < b.length()) {
              if (a.charAt(i) == b.charAt(j)) {
                  j++;
                  count++;
              }
              i++;
          }
          return a.length() + b.length() - 2 * count;
      }
  
      static void reverse(int[] a, int n) {
          for (int i = 0; i < n / 2; i++) {
              int temp = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = temp;
          }
      }
  
      static char get_char(int a) {
          return (char) (a + 'a');
      }
  
      static void dfs(int i, List<List<Integer>> arr, boolean[] visited, int parent) {
          visited[i] = true;
          for (int v : arr.get(i)) {
              if (!visited[v]) {
                  dfs(v, arr, visited, i);
              }
          }
      }
  
      static int find1(List<Integer> a, int val) {
          int ans = -1;
          int l = 0;
          int r = a.size() - 1;
          while (l <= r) {
              int mid = l + (r - l) / 2;
              if (a.get(mid) >= val) {
                  r = mid - 1;
                  ans = mid;
              } else
                  l = mid + 1;
          }
          return ans;
      }
  
      static int find2(List<Integer> a, int val) {
          int l = 0;
          int r = a.size() - 1;
          int ans = -1;
          while (l <= r) {
              int mid = l + (r - l) / 2;
              if (a.get(mid) <= val) {
                  ans = mid;
                  l = mid + 1;
              } else
                  r = mid - 1;
          }
          return ans;
      }
  
      static void dfs(List<List<Integer>> arr, int node, int parent, long[] val) {
          p[node] = parent;
          in_time[node] = count;
          flat_tree[count] = val[node];
          subtree_gcd[node] = val[node];
          count++;
          for (int adj : arr.get(node)) {
              if (adj == parent)
                  continue;
              dfs(arr, adj, node, val);
              subtree_gcd[node] = gcd(subtree_gcd[adj], subtree_gcd[node]);
          }
          out_time[node] = count;
          flat_tree[count] = val[node];
          count++;
      }
  }