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.Arrays;
  import java.util.Stack;
  import java.io.BufferedReader;
  import java.io.FileReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.StringTokenizer;
  import java.util.Random;
  import java.io.FileWriter;
  import java.io.PrintWriter;
  /*
      Solution Created: 21:51:47 21/12/2021
      Custom Competitive programming helper.
  */
  
  public class Main {
  	
  	public static void solve() {
  		int n = in.nextInt();
  		int[] a = in.na(n);
  		int[] f = new int[n+1];
  		for(int i : a) f[i]++;
  		long[] ans = new long[n+1];
  		Arrays.fill(ans, -1);
  		Stack<Integer> leftovers = new Stack<>();
  		long sum = 0;
  		for(int mex = 0; mex<=n; mex++) {
  			ans[mex] = f[mex] + sum;
  			while(f[mex]>1) {
  				leftovers.add(mex);
  				f[mex]--;
  			}
  			if(f[mex]==0) {
  				if(leftovers.isEmpty()) break;
  				sum += mex-leftovers.pop();
  			}
  		}
  		out.printlnArray(ans);
  	}
  	public static void main(String[] args) {
  		in = new Reader();
  		out = new Writer();
  		int t = in.nextInt();
  		while(t-->0) solve();
  		out.exit();
  	}
  	static Reader in; static Writer out;
  
  static class Reader {
  	static BufferedReader br;
  	static StringTokenizer st;
  	
  	public Reader() {
  		this.br = new BufferedReader(new InputStreamReader(System.in));
  	}
  	
  	public Reader(String f){
  		try {
  			this.br = new BufferedReader(new FileReader(f));
  		} catch (IOException e) {
  			e.printStackTrace();
  		}
  	}
  	
  	public int[] na(int n) {
  		int[] a = new int[n];
  		for (int i = 0; i < n; i++) a[i] = nextInt();
  		return a;
  	}
  
  	public double[] nd(int n) {
  		double[] a = new double[n];
  		for (int i = 0; i < n; i++) a[i] = nextDouble();
  		return a;
  	}
  	
  	public long[] nl(int n) {
  		long[] a = new long[n];
  		for (int i = 0; i < n; i++) a[i] = nextLong();
  		return a;
  	}
  
  	public char[] nca() {
  		return next().toCharArray();
  	}
  
  	public String[] ns(int n) {
  		String[] a = new String[n];
  		for (int i = 0; i < n; i++) a[i] = next();
  		return a;
  	}
  
  	public int nextInt() {
  		ensureNext();
  		return Integer.parseInt(st.nextToken());
  	}
  
  	public double nextDouble() {
  		ensureNext();
  		return Double.parseDouble(st.nextToken());
  	}
  
  	public Long nextLong() {
  		ensureNext();
  		return Long.parseLong(st.nextToken());
  	}
  
  	public String next() {
  		ensureNext();
  		return st.nextToken();
  	}
  	
  	public String nextLine() {
  		try {
  			return br.readLine();
  		} catch (Exception e) {
  			e.printStackTrace();
  			return null;
  		}
  	}
  	
  	private void ensureNext() {
  		if (st == null || !st.hasMoreTokens()) {
  			try {
  				st = new StringTokenizer(br.readLine());
  			} catch (IOException e) {
  				e.printStackTrace();
  			}
  		}
  	}
  }
  
  static class Util{
  		private static Random random = new Random();
  		static long[] fact;
  		
  		public static void initFactorial(int n, long mod) {
  			fact = new long[n+1];
  			fact[0] = 1;
  			for (int i = 1; i < n+1; i++) fact[i] = (fact[i - 1] * i) % mod;
  		}
  		
  		public static long modInverse(long a, long MOD) {
  			long[] gcdE = gcdExtended(a, MOD);
  			if (gcdE[0] != 1) return -1; // Inverted doesn't exist
  			long x = gcdE[1];
  			return (x % MOD + MOD) % MOD;
  		}
  		
  		public static long[] gcdExtended(long p, long q) {
  			if (q == 0) return new long[] { p, 1, 0 };
  			long[] vals = gcdExtended(q, p % q);
  			long tmp = vals[2];
  			vals[2] = vals[1] - (p / q) * vals[2];
  			vals[1] = tmp;
  			return vals;
  		}
  		
  		public static long nCr(int n, int r, long MOD) {
  			if (r == 0) return 1;
  			return (fact[n] * modInverse(fact[r], MOD) % MOD * modInverse(fact[n - r], MOD) % MOD) % MOD;
  		}
  		
  		public static long nCr(int n, int r) {
  			return (fact[n]/fact[r])/fact[n-r];
  		}
  		
  		public static long nPr(int n, int r, long MOD) {
  			if (r == 0) return 1;
  			return (fact[n] * modInverse(fact[n - r], MOD) % MOD) % MOD;
  		}
  		public static long nPr(int n, int r) {
  			return fact[n]/fact[n-r];
  		}
  		
  		public static boolean isPrime(int n) { 
  	        if (n <= 1) return false; 
  	        if (n <= 3) return true; 
  	        if (n % 2 == 0 || n % 3 == 0) return false; 
  	        for (int i = 5; i * i <= n; i = i + 6) 
  	            if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	        return true; 
  	    }
  		
  	    public static boolean[] getSieve(int n) {
  	        boolean[] isPrime = new boolean[n+1];
  	        for (int i = 2; i <= n; i++) isPrime[i] = true;
  	        for (int i = 2; i*i <= n; i++) if (isPrime[i]) 
  	                for (int j = i; i*j <= n; j++) isPrime[i*j] = false;
  	        return isPrime;
  	    }
  	    
  	    static long pow(long x, long pow, long mod){
  	    	long res = 1;
  	    	x = x % mod;
  	    	if (x == 0) return 0;
  	    	while (pow > 0){
  	    		if ((pow & 1) != 0) res = (res * x) % mod;
  	        	pow >>= 1;
  	        	x = (x * x) % mod;
  	    	}
  	    	return res;
  	    }
  	    
  	    public static int gcd(int a, int b) { 
  	    	int tmp = 0;
  	    	while(b != 0) {
  	    		tmp = b;
  	    		b = a%b;
  	    		a = tmp;
  	    	}
  	    	return a;
  	    }
  	    
  	    public static long gcd(long a, long b) { 
  	    	long tmp = 0;
  	    	while(b != 0) {
  	    		tmp = b;
  	    		b = a%b;
  	    		a = tmp;
  	    	}
  	    	return a;
  	    }
  	    
  	    public static int random(int min, int max) {
  	    	return random.nextInt(max-min+1)+min;
  	    }
  	    
  		public static void dbg(Object... o) { 
  			System.out.println(Arrays.deepToString(o)); 
  		}
  		
  		public static void reverse(int[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				int tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(int[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(long[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				long tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(long[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(float[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				float tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(float[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(double[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				double tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(double[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(char[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				char tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(char[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static <T> void reverse(T[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				T tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static <T> void reverse(T[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void shuffle(int[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            int t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  		
  	    public static void shuffle(long[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            long t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(float[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            float t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(double[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            double t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(char[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            char t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static <T> void shuffle(T[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            T t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  		public static void sortArray(int[] a) {
  	        shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(long[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(float[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(double[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(char[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static <T extends Comparable<T>> void sortArray(T[] a) {
  	        Arrays.sort(a);
  	    }
  		
  		public static int[][] rotate90(int[][] a){
  			int n = a.length, m = a[0].length;
  			int[][] ans = new int[m][n];
  			for(int i = 0; i<n; i++) for(int j = 0; j<m; j++) ans[m-j-1][i] = a[i][j];
  			return ans;
  		}
  		
  		public static char[][] rotate90(char[][] a){
  			int n = a.length, m = a[0].length;
  			char[][] ans = new char[m][n];
  			for(int i = 0; i<n; i++) for(int j = 0; j<m; j++) ans[m-j-1][i] = a[i][j];
  			return ans;
  		}
  	}
  
  static class Writer {
  	private PrintWriter pw;
  	public Writer(){
  		pw = new PrintWriter(System.out);
  	}
  	
  	public Writer(String f){
  		try {
  			pw = new PrintWriter(new FileWriter(f));
  		} catch (IOException e) {
  			e.printStackTrace();
  		}
  	}
  	
  	public void yesNo(boolean condition) {
  		println(condition?"YES":"NO");
  	}
  	
  	public void printArray(int[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  	}
  	
  	public void printlnArray(int[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  		pw.println();
  	}
  	
  	public void printArray(long[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  	}
  	
  	public void printlnArray(long[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  		pw.println();
  	}
  	
  	public void print(Object o) {
  		pw.print(o.toString());
  	}
  	
  	public void println(Object o) {
  		pw.println(o.toString());
  	}
  	
  	public void println() {
  		pw.println();
  	}
  	
  	public void flush() {
  		pw.flush();
  	}
  	public void exit() {
  		pw.close();
  	}
  }
  }
  