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.math.*;
  import java.sql.Array;
  import java.sql.ResultSet;
  import java.sql.SQLException;
  import java.sql.SQLIntegrityConstraintViolationException;
  
  
  
  public class Main {
  	 private static class MyScanner {
  	        private static final int BUF_SIZE = 2048;
  	        BufferedReader br;
  	 
  	        private MyScanner() {
  	            br = new BufferedReader(new InputStreamReader(System.in));
  	        }
  	 
  	        private boolean isSpace(char c) {
  	            return c == '\n' || c == '\r' || c == ' ';
  	        }
  	 
  	        String next() {
  	            try {
  	                StringBuilder sb = new StringBuilder();
  	                int r;
  	                while ((r = br.read()) != -1 && isSpace((char)r));
  	                if (r == -1) {
  	                    return null;
  	                }
  	 
  	                sb.append((char) r);
  	                while ((r = br.read()) != -1 && !isSpace((char)r)) {
  	                    sb.append((char)r);
  	                }
  	                return sb.toString();
  	            } catch (IOException e) {
  	                e.printStackTrace();
  	            }
  	            return null;
  	        }
  	 
  	        int nextInt() {
  	            return Integer.parseInt(next());
  	        }
  	 
  	        long nextLong() {
  	            return Long.parseLong(next());
  	        }
  	 
  	        double nextDouble() {
  	            return Double.parseDouble(next());
  	        }
  	    }
  	  static class Reader{
  		  
  			BufferedReader br;
  			StringTokenizer st;
  			public Reader() {
  				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; 
  		    } 
  		}
  	 
  	  static long mod = (long)(1e9 + 7);
  	 
  	static void sort(long[] arr ) {
  		 ArrayList<Long> al = new ArrayList<>();
  		 for(long e:arr) al.add(e);
  		 Collections.sort(al);
  		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
  	 }
  	static void sort(int[] arr ) {
  		 ArrayList<Integer> al = new ArrayList<>();
  		 for(int e:arr) al.add(e);
  		 Collections.sort(al);
  		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
  	 }
  	
  	static void sort(char[] arr) {
  		ArrayList<Character> al = new ArrayList<Character>();
  		for(char cc:arr) al.add(cc);
  		Collections.sort(al);
  		for(int i = 0 ;i<arr.length ;i++) arr[i] = al.get(i);
  	}
  
  	static long mod_mul(  long... a) {
  		long ans = a[0]%mod;
  		for(int i = 1 ; i<a.length ; i++) {
  			ans = (ans * (a[i]%mod))%mod;
  		}
  		
  		return ans;
  	}
  	static long mod_sum( long... a) {
  		long ans = 0;
  		for(long e:a) {
  			ans = (ans + e)%mod;
  		}
  		return ans;
  	}
  	 static long gcd(long a, long b)
  	  {      
  	     if (b == 0)
  	        return a;
  	     return gcd(b, a % b); 
  	  }
  	 static boolean[] prime(int num) {
  			boolean[] bool = new boolean[num];
  		     
  		      for (int i = 0; i< bool.length; i++) {
  		         bool[i] = true;
  		      }
  		      for (int i = 2; i< Math.sqrt(num); i++) {
  		         if(bool[i] == true) {
  		            for(int j = (i*i); j<num; j = j+i) {
  		               bool[j] = false;
  		            }
  		         }
  		      }
  		      if(num >= 0) {
  		    	  bool[0] = false;
  		    	  bool[1] = false;
  		      }
  		      
  		      return bool;
  		}
  
  	 static long modInverse(long a, long m)
  	    {
  	        long g = gcd(a, m);
  	       
  	          return   power(a, m - 2, m);
  	        
  	    }
  	   static long lcm(long a , long b) {
  		   return (a*b)/gcd(a, b);
  	   }
  	   static int lcm(int a , int b) {
  		   return (int)((a*b)/gcd(a, b));
  	   }
  	 static long power(long x, long y, long m){
  	        if (y == 0) return 1; long p = power(x, y / 2, m) % m; p = (int)((p * (long)p) % m);
  	        if (y % 2 == 0) return p; else return (int)((x * (long)p) % m); }
  	   
       static class Combinations{
  	    	 private long[] z;
  	    	 private long[] z1;
  	    	 private long[] z2;
  	    	 private long mod;
  	    	  public Combinations(long N , long mod) {
  	    		  this.mod = mod;
  				z = new long[(int)N+1];
  				z1 = new long[(int)N+1];
  				z[0] = 1;
  				for(int i =1 ; i<=N ; i++) z[i] = (z[i-1]*i)%mod;
  			     z2 = new long[(int)N+1];
  				z2[0] = z2[1] = 1;
  			    for (int i = 2; i <= N; i++)
  			        z2[i] = z2[(int)(mod % i)] * (mod - mod / i) % mod;
  			    
  			    
  			    z1[0] = z1[1] = 1;
  			    
  			    for (int i = 2; i <= N; i++)
  			        z1[i] = (z2[i] * z1[i - 1]) % mod;
  			}
  	    	  long fac(long n) {
  	    		  return z[(int)n];
  	    	  }
  	    	  long invrsNum(long n) {
  	    		  return z2[(int)n];
  	    	  }
  	    	  long invrsFac(long n) {
  	    		  return invrsFac((int)n);
  	    	  }
  	    	  long ncr(long N, long R)
  	    	  {		if(R<0 || R>N ) return 0;
  	    		    long ans = ((z[(int)N] * z1[(int)R])
  	    		              % mod * z1[(int)(N - R)])
  	    		             % mod;
  	    		    return ans;
  	    		}
  	      }
  	      static class DisjointUnionSets {
  			    int[] rank, parent;
  			    int n;
  			  
  			    public DisjointUnionSets(int n)
  			    {
  			        rank = new int[n];
  			        parent = new int[n];
  			        this.n = n;
  			        makeSet();
  			    }
  			  
  			    void makeSet()
  			    {
  			        for (int i = 0; i < n; i++) {
  			          
  			            parent[i] = i;
  			        }
  			    }
  			  
  			    int find(int x)
  			    {
  			        if (parent[x] != x) {
  			        
  			            parent[x] = find(parent[x]);
  			  
  			        }
  			  
  			        return parent[x];
  			    }
  			  
  			    void union(int x, int y)
  			    {
  			        int xRoot = find(x), yRoot = find(y);
  			  
  			        if (xRoot == yRoot)
  			            return;
  			  
  			        if (rank[xRoot] < rank[yRoot])
  			  
  			            parent[xRoot] = yRoot;
  			  
  			        else if (rank[yRoot] < rank[xRoot])
  			  
  			            parent[yRoot] = xRoot;
  			  
  			        else
  			        {
  			            parent[yRoot] = xRoot;
  			  
  			            rank[xRoot] = rank[xRoot] + 1;
  			        }
  			    }
  			}
  	      static int max(int... a ) {
  	    	  int max = a[0];
  	    	  for(int e:a) max = Math.max(max, e);
  	    	  return max;
  	      }
  	      static long max(long... a ) {
  	    	  long max = a[0];
  	    	  for(long e:a) max = Math.max(max, e);
  	    	  return max;
  	      }
  	      static int min(int... a ) {
  	    	  int min = a[0];
  	    	  for(int e:a) min = Math.min(e, min);
  	    	  return min;
  	      }
  	      static long min(long... a ) {
  	    	  long min = a[0];
  	    	  for(long e:a) min = Math.min(e, min);
  	    	  return min;
  	      }
  	      static int[] KMP(String str) {
  	    	  int n = str.length();
  	    	  int[] kmp = new int[n];
  	    	  for(int i = 1 ; i<n ; i++) {
  	    		  int j = kmp[i-1];
  	    		  while(j>0 && str.charAt(i) != str.charAt(j)) {
  	    			  j = kmp[j-1];
  	    		  }
  	    		  if(str.charAt(i) == str.charAt(j)) j++;
  	    		  kmp[i] = j;
  	    	  }
  	    	  
  	    	  return kmp;
  	      }
  	      
  	      
  /************************************************ Query **************************************************************************************/	  
  	 
  /***************************************** 		Sparse Table	********************************************************/
  	      static class SparseTable{
  	    		
  	    		private long[][] st;
  	    		
  	    		SparseTable(long[] arr){
  	    			int n = arr.length;
  	    			st = new long[n][25];
  	    			log = new int[n+2];
  	    			build_log(n+1);
  	    			build(arr);
  	    		}
  	    		
  	    		private void build(long[] arr) {
  	    			int n = arr.length;
  	    			
  	    			for(int i = n-1 ; i>=0 ; i--) {
  	    				for(int j = 0 ; j<25 ; j++) {
  	    					int r = i + (1<<j)-1;
  	    					if(r>=n) break;
  	    					if(j == 0 ) st[i][j] = arr[i];
  	    					else st[i][j] = Math.min(st[i][j-1] , st[ i + ( 1 << (j-1) ) ][ j-1 ] );
  	    				}
  	    			}
  	    		}
  	    		public long gcd(long a  ,long b) {
  	    			if(a == 0) return b;
  	    			return gcd(b%a , a);
  	    		}
  	    		public long query(int l ,int r) {
  	    			int w = r-l+1;
  	    			int power = log[w];
  	    			return Math.min(st[l][power],st[r - (1<<power) + 1][power]);
  	    		}
  	    		private int[] log;
  	    		void build_log(int n) {
  	    			log[1] = 0;
  	    			for(int i = 2 ; i<=n ; i++) {
  	    				log[i] = 1 + log[i/2];
  	    			}
  	    		}
  	    	}
  	      
  	      
  /********************************************************	Segement Tree	*****************************************************/
  /**
  	 	 static class SegmentTree{
  			 long[] tree;
  			 long[] arr;
  			 int n;
  			 SegmentTree(long[] arr){
  				 this.n = arr.length;
  				 tree = new long[4*n+1];
  				 this.arr = arr;
  				 buildTree(0, n-1, 1);
  			 }
  			 
  			 
  			  void buildTree(int s ,int e  ,int index ) {
  					if(s == e) {
  						tree[index] = arr[s];
  						return;
  					}
  				
  					int mid = (s+e)/2;
  					
  					buildTree( s,  mid, 2*index);
  					buildTree( mid+1, e, 2*index+1);
  					
  					tree[index] = Math.min(tree[2*index] , tree[2*index+1]);
  				}
  			  
  			 long query(int si ,int ei) {
  				 return query(0 ,n-1 , si ,ei , 1   );
  			 }
  			 private long query( int ss ,int se ,int qs , int qe,int index) {
  					
  					if(ss>=qs && se<=qe) return tree[index];
  					
  					if(qe<ss || se<qs) return (long)(1e17);
  					
  					int mid = (ss + se)/2;
  					long left = query( ss , mid , qs ,qe , 2*index);
  					long right= query(mid + 1 , se , qs ,qe , 2*index+1);
  					return Math.min(left, right);
  				}
  			 public void update(int index , int val) {
  				 arr[index] = val;
  				 for(long e:arr) System.out.print(e+" ");
  				 update(index , 0 , n-1 , 1);
  			 }
  			 private void update(int id ,int si , int ei , int index) {
  				 if(id < si || id>ei) return;
  				 if(si == ei ) { 
  					 tree[index] = arr[id];
  					 return;
  				 }
  				 if(si > ei) return;
  				 int mid = (ei + si)/2;
  					
  					update( id,  si, mid , 2*index);
  					update( id , mid+1, ei , 2*index+1);
  					
  					tree[index] = Math.min(tree[2*index] ,tree[2*index+1]);
  			 }
  			  
  		 }
  		 */
  
  /* ***************************************************************************************************************************************************/	 
  	 
  //	      static MyScanner sc = new MyScanner(); // only in case of less memory
  	      static Reader sc = new Reader();
  	 static StringBuilder sb = new StringBuilder();
  	 public static void main(String args[]) throws IOException {
  
  		 int tc = 1;
  		  tc = sc.nextInt();
  
  		 for(int i = 1 ; i<=tc ; i++) {
  
  //			 sb.append("Case #" + i + ": "  );	// During KickStart && HackerCup
  			 TEST_CASE();
  			  
  		 }
  		 System.out.print(sb);
  	 }
  	 static class Pair{
  		 int x;
  		 int y;
  		 Pair(int x , int y){
  			 this.x = x;
  			 this.y = y;
  		 }
  		 public String toString() {
  			 return "{"+this.x+","+this.y+"}";
  		 }
  	 }
  	 static void TEST_CASE() {
  		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) {
  			sb.append(e+" ");
  		}
  		sb.append("\n");
  	 }
  	 
  	 
  }
  /*******************************************************************************************************************************************************/
  
  /**
   
   	
   	
   	
   
   
   */
  
   
  
  