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.*;
  
  public class Main {
  	static StringBuilder sb;
  	static dsu dsu;
  	static long fact[];
  	static int mod = (int) (1e9 + 7);
      static long[] get(HashMap<Integer,Integer>hm,int n){
          Stack<Pair> s=new Stack<>();
          long []ans=new long[n+1];
          ans[0]=hm.containsKey(0)?0:-1;
          if(ans[0]==0&&hm.get(0)>1){
              s.push(new Pair(0,hm.get(0)-1));
          }
          for(int i=1;i<=n;i++){
              if(ans[i-1]==-1){
                  ans[i]=-1;
                  continue;
              }
              if(hm.containsKey(i)){
                  if(hm.get(i)>1){
                      ans[i]=0;
                      s.push(new Pair(i,hm.get(i)-1));
                  }
                  else{
                      ans[i]=0;
                  }
              }
              else{
                  if(s.size()==0)ans[i]=-1;
                  else{
                      Pair p=s.pop();
                      ans[i]=i-p.val;
                      p.f--;
                      if(p.f>0)s.push(p);
                      
                      
                  }
              }
              
          if(ans[i]!=-1&&ans[i-1]!=-1)ans[i]+=ans[i-1];
          }
          return ans;
      }
  	static void solve() {
  	int n=i();
  	int[]arr=new int[n];
  	HashMap<Integer,Integer> hm=new HashMap<>();
  
  	for(int i=0;i<n;i++){
  	arr[i]=i(); 
  
  	  hm.put((int)arr[i],hm.getOrDefault((int)arr[i],0)+1);
  	}
  
      long[]toAdd=get(hm,n);
  
  //1 1 2 2 1 0 2 6 
  	int[]ps=new int[n+1];
      for(int i=1;i<=n;i++){
          ps[i]=ps[i-1]+hm.getOrDefault((i-1),0);
      }
  	long[]ans=new long[n+1];
  	sb.append(hm.getOrDefault(0,0)+" ");
  	for(int mex=1;mex<=n;mex++){
  	    int idx=(int)mex;
  	    if(ps[idx]<mex||toAdd[idx-1]==-1){
  	        ans[idx]=-1;
  	        sb.append(ans[idx]+" ");
  	        continue;
  	    }
  	    ans[idx]=(long)hm.getOrDefault(mex,0);
  	   ans[idx]+=toAdd[idx-1];
  	    sb.append(ans[idx]+" ");
  	}
  	
  	sb.append("\n");
  	}
  
  	public static void main(String[] args) {
  		sb = new StringBuilder();
  		int test = i();
  		while (test-- > 0) {
  			solve();
  		}
  		System.out.println(sb);
  
  	}
  
  	/*
  	 * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
  	 * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
  	 */
  //**************NCR%P******************	 
  	static long ncr(int n, int r) {
  		if (r > n)
  			return (long) 0;
  
  		long res = fact[n] % mod;
  		// System.out.println(res);
  		res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
  		res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
  		// System.out.println(res);
  		return res;
  
  	}
  
  	static long p(long x, long y)// POWER FXN //
  	{
  		if (y == 0)
  			return 1;
  
  		long res = 1;
  		while (y > 0) {
  			if (y % 2 == 1) {
  				res = (res * x) % mod;
  				y--;
  			}
  
  			x = (x * x) % mod;
  			y = y / 2;
  
  		}
  		return res;
  	}
  
  //**************END******************
  
  	// *************Disjoint set
  	// union*********//
  	static class dsu {
  		int parent[];
  
  		dsu(int n) {
  			parent = new int[n];
  			for (int i = 0; i < n; i++)
  				parent[i] = -1;
  		}
  
  		int find(int a) {
  			if (parent[a] < 0)
  				return a;
  			else {
  				int x = find(parent[a]);
  				parent[a] = x;
  				return x;
  			}
  		}
  
  		void merge(int a, int b) {
  			a = find(a);
  			b = find(b);
  			if (a == b)
  				return;
  			parent[b] = a;
  		}
  	}
  
  //**************PRIME FACTORIZE **********************************//
  	static TreeMap<Integer, Integer> prime(long n) {
  		TreeMap<Integer, Integer> h = new TreeMap<>();
  		long num = n;
  		for (int i = 2; i <= Math.sqrt(num); i++) {
  			if (n % i == 0) {
  				int nt = 0;
  				while (n % i == 0) {
  					n = n / i;
  					nt++;
  				}
  				h.put(i, nt);
  			}
  		}
  		if (n != 1)
  			h.put((int) n, 1);
  		return h;
  
  	}
  
  //****CLASS PAIR ************************************************
  	static class Pair  {
  		int val;
  		int f;
  
  		Pair(int val, int f) {
  			this.val = val;
  			this.f = f;
  		}
  
  	
  
  	}
  //****CLASS PAIR **************************************************
  
  	static class InputReader {
  		private InputStream stream;
  		private byte[] buf = new byte[1024];
  		private int curChar;
  		private int numChars;
  		private SpaceCharFilter filter;
  
  		public InputReader(InputStream stream) {
  			this.stream = stream;
  		}
  
  		public int read() {
  			if (numChars == -1)
  				throw new InputMismatchException();
  			if (curChar >= numChars) {
  				curChar = 0;
  				try {
  					numChars = stream.read(buf);
  				} catch (IOException e) {
  					throw new InputMismatchException();
  				}
  				if (numChars <= 0)
  					return -1;
  			}
  			return buf[curChar++];
  		}
  
  		public int Int() {
  			int c = read();
  			while (isSpaceChar(c))
  				c = read();
  			int sgn = 1;
  			if (c == '-') {
  				sgn = -1;
  				c = read();
  			}
  			int res = 0;
  			do {
  				if (c < '0' || c > '9')
  					throw new InputMismatchException();
  				res *= 10;
  				res += c - '0';
  				c = read();
  			} while (!isSpaceChar(c));
  			return res * sgn;
  		}
  
  		public String String() {
  			int c = read();
  			while (isSpaceChar(c))
  				c = read();
  			StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(c);
  				c = read();
  			} while (!isSpaceChar(c));
  			return res.toString();
  		}
  
  		public boolean isSpaceChar(int c) {
  			if (filter != null)
  				return filter.isSpaceChar(c);
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  
  		public String next() {
  			return String();
  		}
  
  		public interface SpaceCharFilter {
  			public boolean isSpaceChar(int ch);
  		}
  	}
  
  	static class OutputWriter {
  		private final PrintWriter writer;
  
  		public OutputWriter(OutputStream outputStream) {
  			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
  		}
  
  		public OutputWriter(Writer writer) {
  			this.writer = new PrintWriter(writer);
  		}
  
  		public void print(Object... objects) {
  			for (int i = 0; i < objects.length; i++) {
  				if (i != 0)
  					writer.print(' ');
  				writer.print(objects[i]);
  			}
  		}
  
  		public void printLine(Object... objects) {
  			print(objects);
  			writer.println();
  		}
  
  		public void close() {
  			writer.close();
  		}
  
  		public void flush() {
  			writer.flush();
  		}
  	}
  
  	static InputReader in = new InputReader(System.in);
  	static OutputWriter out = new OutputWriter(System.out);
  
  	public static long[] sort(long[] a2) {
  		int n = a2.length;
  		ArrayList<Long> l = new ArrayList<>();
  		for (long i : a2)
  			l.add(i);
  		Collections.sort(l);
  		for (int i = 0; i < l.size(); i++)
  			a2[i] = l.get(i);
  		return a2;
  	}
  
  	public static char[] sort(char[] a2) {
  		int n = a2.length;
  		ArrayList<Character> l = new ArrayList<>();
  		for (char i : a2)
  			l.add(i);
  		Collections.sort(l);
  		for (int i = 0; i < l.size(); i++)
  			a2[i] = l.get(i);
  		return a2;
  	}
  
  	public static long pow(long x, long y) {
  		long res = 1;
  		while (y > 0) {
  			if (y % 2 != 0) {
  				res = (res * x);// % modulus;
  				y--;
  
  			}
  			x = (x * x);// % modulus;
  			y = y / 2;
  		}
  		return res;
  	}
  
  //GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  	public static long gcd(long x, long y) {
  		if (x == 0)
  			return y;
  		else
  			return gcd(y % x, x);
  	}
  	// ******LOWEST COMMON MULTIPLE
  	// *********************************************
  
  	public static long lcm(long x, long y) {
  		return (x * (y / gcd(x, y)));
  	}
  
  //INPUT PATTERN********************************************************
  	public static int i() {
  		return in.Int();
  	}
  
  	public static long l() {
  		String s = in.String();
  		return Long.parseLong(s);
  	}
  
  	public static String s() {
  		return in.String();
  	}
  
  	public static int[] readArrayi(int n) {
  		int A[] = new int[n];
  		for (int i = 0; i < n; i++) {
  			A[i] = i();
  		}
  		return A;
  	}
  
  	public static long[] readArray(long n) {
  		long A[] = new long[(int) n];
  		for (int i = 0; i < n; i++) {
  			A[i] = l();
  		}
  		return A;
  	}
  
  }