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.lang.*;
  // import java.math.*;
  
  public class Main {
      static FastReader sc=new FastReader();
  	static PrintWriter out=new PrintWriter(System.out);
  	static long mod=1000000007;
  	// static long mod=998244353;
  	static int MAX=Integer.MAX_VALUE;
  	static int MIN=Integer.MIN_VALUE;
  	static long MAXL=Long.MAX_VALUE;
  	static long MINL=Long.MIN_VALUE;
  	static ArrayList<Integer> graph[];
  	static long fact[];
  	static StringBuffer sb;
  	static ArrayList<Integer> seg[];
  	static int lazy[];//lazy propagation is used in case of range updates.
  	static long dp[][];
  	public static void main (String[] args) throws java.lang.Exception
  	{
  		// code goes here
  		int t=I();
  		outer:while(t-->0)
  		{
  			int n=I();
  			int a[]=new int[n];
  			HashMap<Integer,Integer> hm=new HashMap<>();
  			for(int i=0;i<n;i++){
  				a[i]=I();
  				hm.put(a[i],hm.getOrDefault(a[i],0)+1);
  			}
  			ArrayList<Integer> arr=new ArrayList<>();
  			boolean flag=true;
  			long s=0;
  			for(int i=0;i<=n;i++){
  				if(!flag)out.print("-1 ");
  				else{
  					int fr=hm.getOrDefault(i,0);
  					out.print((s+fr)+" ");
  					if(fr==1){
  						continue;
  					}
  					if(fr==0){
  						if(arr.size()==0){
  							flag=false;
  							continue;
  						}
  						int p=arr.remove(arr.size()-1);
  						s+=i-p;
  					}else{
  						while(fr-->1){
  							arr.add(i);
  						}
  					}
  				}
  			}out.println();
  		}
  		out.close();
  	}
  	public static class pair
      {
      	long a;
      	long b;
      	public pair(long aa,long bb)
      	{
      	    a=aa;
      	    b=bb;
      	}
      }
  	public static class myComp implements Comparator<pair>
  	{
  		//sort in ascending order.
  		// public int compare(pair p1,pair p2)
  		// {
  		// 	if(p1.a==p2.a)
      	//     return 0;
      	//     else if(p1.a<p2.a)
      	//     return -1;
      	//     else
      	//     return 1;
  		// }
  		// sort in descending order.
  		public int compare(pair p1,pair p2)
      	{
      	    if(p1.a==p2.a)
      	    return 0;
      	    else if(p1.a<p2.a)
      	    return 1;
      	    else
      	    return -1;
      	}
  	}
  	public static void DFS(int s,boolean visited[])
  	{
  		visited[s]=true;
  		for(int i:graph[s]){
  			if(!visited[i]){
  				DFS(i,visited);
  			}
  		}
  	}
  	public static void setGraph(int n,int m)throws IOException
  	{
  		graph=new ArrayList[n+1];
  		for(int i=0;i<=n;i++){
  			graph[i]=new ArrayList<>();
  		}
  		for(int i=0;i<m;i++){
  			int u=I(),v=I();
  			graph[u].add(v);
  			graph[v].add(u);
  		}
  	}
  
  	//LOWER_BOUND and UPPER_BOUND functions
  
  	//It returns answer according to zero based indexing.
  	public static int lower_bound(int arr[],int X,int start, int end)   //start=0,end=n-1
  	{
  		if(start>end)return -1;
  		if(arr[arr.length-1]<X)return end;
  		if(arr[0]>X)return -1;
  		int left=start,right=end;
  		while(left<right){
  			int mid=(left+right)/2;
  			if(arr[mid]==X){                                      //Returns last index of lower bound value.
  				if(mid<end && arr[mid+1]==X){
  					left=mid+1;
  				}else{
  					return mid;
  				}
  			}
  			// if(arr[mid]==X){                                   //Returns first index of lower bound value.
  			// 	if(mid>start && arr[mid-1]==X){
  			// 		right=mid-1;
  			// 	}else{
  			// 		return mid;
  			// 	}
  			// }
  			else if(arr[mid]>X){
  				if(mid>start && arr[mid-1]<X){
  					return mid-1;
  				}else{
  					right=mid-1;
  				}
  			}else{
  				if(mid<end && arr[mid+1]>X){
  					return mid;
  				}else{
  					left=mid+1;
  				}
  			}
  		}
  		return left;
  	}
  	//It returns answer according to zero based indexing.
  	public static int upper_bound(ArrayList<Integer> arr,int X,int start,int end)			//start=0,end=n-1
  	{
  		if(arr.get(0)>=X)return start;
  		if(arr.get(arr.size()-1)<X)return -1;
  		int left=start,right=end;
  		while(left<right){
  			int mid=(left+right)/2;
  			if(arr.get(mid)==X){                                   //returns first index of upper bound value.
  				if(mid>start && arr.get(mid-1)==X){
  					right=mid-1;
  				}else{
  					return mid;
  				}
  			}
  			// if(arr[mid]==X){									//returns last index of upper bound value.
  			// 	if(mid<end && arr[mid+1]==X){
  			// 		left=mid+1;
  			// 	}else{
  			// 		return mid;
  			// 	}
  			// }
  			else if(arr.get(mid)>X){
  				if(mid>start && arr.get(mid-1)<X){
  					return mid;
  				}else{
  					right=mid-1;
  				}
  			}else{
  				if(mid<end && arr.get(mid+1)>X){
  					return mid+1;
  				}else{
  					left=mid+1;
  				}
  			}
  		}
  		return left;
  	}
  
  	//END
  	
  	public static long nPr(int n,int r)
  	{
  		long ans=divide(fact(n),fact(n-r),mod);
  		return ans;
  	}
  	public static long nCr(int n,int r)
  	{
  		long ans=divide(fact[n],mul(fact[n-r],fact[r]),mod);
  		return ans;
  	}
  	public static long kadane(long a[],int n)  //largest sum subarray
  	{
  		long max_sum=Long.MIN_VALUE,max_end=0;
  		for(int i=0;i<n;i++){
  			max_end+=a[i];
  			if(max_sum<max_end){max_sum=max_end;}
  			if(max_end<0){max_end=0;}
  		}
  		return max_sum;
  	}
  
  	public static boolean isSorted(int a[])
  	{
  		int n=a.length;
  		for(int i=0;i<n-1;i++){
  			if(a[i]>a[i+1])return false;
  		}
  		return true;
  	}
  	public static boolean isSorted(long a[])
  	{
  		int n=a.length;
  		for(int i=0;i<n-1;i++){
  			if(a[i]>a[i+1])return false;
  		}
  		return true;
  	}
  	public static int computeXOR(int n) //compute XOR of all numbers between 1 to n.
      {
          if (n % 4 == 0)
              return n;
          if (n % 4 == 1)
              return 1;
          if (n % 4 == 2)
              return n + 1;
          return 0;
      }
  	public static ArrayList<Integer> primeSieve(int n)
  	{
  	    ArrayList<Integer> arr=new ArrayList<>();
  	    boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
          prime[i] = true;
          for (int p = 2; p * p <= n; p++)
          {
              if (prime[p] == true)
              {
                  for (int i = p * p; i <= n; i += p)
                  prime[i] = false;
              }
          }
          for (int i = 2; i <= n; i++)
          {
              if (prime[i] == true)
              arr.add(i);
          }
          return arr;
  	}
  	
  	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
  	public static class FenwickTree
  	{
  		int farr[];
  		int n;
  		public FenwickTree(int c)
  		{
  			n=c+1;
  			farr=new int[n];
  		}
  		// public void update_range(int l,int r,long p)
  		// {
  		// 	update(l,p);
  		// 	update(r+1,(-1)*p);
  		// }
  		public void update(int x,int p)
  		{
  			for(;x<n;x+=x&(-x))
  			{
  				farr[x]+=p;
  			}
  		}
  		public long get(int x)
  		{
  			long ans=0;
  			for(;x>0;x-=x&(-x))
  			{
  				ans=ans+farr[x];
  			}
  			return ans;
  		}
  	}
  	//Disjoint Set Union
  	public static class DSU
  	{
  	    int par[],rank[];
  	    public DSU(int c)
  	    {
  	        par=new int[c+1];
  	        rank=new int[c+1];
  	        for(int i=0;i<=c;i++)
  	        {
  	            par[i]=i;
  	            rank[i]=0;
  	        }
  	    }
  	    public int find(int a)
  	    {
  	        if(a==par[a])
  	        return a;
  	        return par[a]=find(par[a]);
  	    }
  	    public void union(int a,int b)
  	    {
  	        int a_rep=find(a),b_rep=find(b);
  	        if(a_rep==b_rep)
  	        return;
  	        if(rank[a_rep]<rank[b_rep])
  	        par[a_rep]=b_rep;
  	        else if(rank[a_rep]>rank[b_rep])
  	        par[b_rep]=a_rep;
  	        else
  	        {
  	            par[b_rep]=a_rep;
  	            rank[a_rep]++;
  	        }
  	    }
  	}
  
  	//Segment Tree Code
  	public static void buildTree(int a[],int si,int ss,int se)
  	{
  		if(ss==se){
  			seg[si].add(a[ss]);
  			return;
  		}
  		int mid=(ss+se)/2;
  		buildTree(a,2*si+1,ss,mid);
  		buildTree(a,2*si+2,mid+1,se);
  		merge(seg[si],seg[2*si+1],seg[2*si+2]);
  	}
  	public static void merge(ArrayList<Integer> f,ArrayList<Integer> a,ArrayList<Integer> b)
  	{
  		int i=0,j=0;
  		while(i<a.size() && j<b.size()){
  			if(a.get(i)<=b.get(j)){
  				f.add(a.get(i));
  				i++;
  			}else{
  				f.add(b.get(j));
  				j++;
  			}
  		}
  		while(i<a.size()){
  			f.add(a.get(i));
  			i++;
  		}
  		while(j<b.size()){
  			f.add(b.get(j));
  			j++;
  		}
  	}
  	// public static void update(int si,int ss,int se,int qs,int qe)
  	// {
  	// 	if(lazy[si]!=0){
  	// 		int dx=lazy[si];
  	// 		if(ss!=se){
  	// 			lazy[2*si+1]+=dx;
  	// 			lazy[2*si+2]+=dx;
  	// 		}
  	// 		dx%=3;
  	// 		for(int i=0;i<dx;i++){
  	// 			int temp=seg[si].a;
  	// 			seg[si].a=seg[si].c;
  	// 			seg[si].c=seg[si].b;
  	// 			seg[si].b=temp;
  	// 		}
  	// 		lazy[si]=0;
  	// 	}
  	// 	if(se<qs || ss>qe)return;
  	// 	if(ss>=qs && se<=qe){
  	// 		int dx=1;
  	// 		if(ss!=se){
  	// 			lazy[2*si+1]+=dx;
  	// 			lazy[2*si+2]+=dx;
  	// 		}
  	// 		// for(int i=0;i<dx;i++){
  	// 			int temp=seg[si].a;
  	// 			seg[si].a=seg[si].c;
  	// 			seg[si].c=seg[si].b;
  	// 			seg[si].b=temp;
  	// 		// }
  	// 		return;
  	// 	}
  	// 	int mid=(ss+se)/2;
  	// 	update(2*si+1,ss,mid,qs,qe);
  	// 	update(2*si+2,mid+1,se,qs,qe);
  	// 	seg[si].a=seg[2*si+1].a+seg[2*si+2].a;
  	// 	seg[si].b=seg[2*si+1].b+seg[2*si+2].b;
  	// 	seg[si].c=seg[2*si+1].c+seg[2*si+2].c;
  	// }
  	public static int query(int si,int ss,int se,int qs,int qe,int val)
  	{
  		// if(lazy[si]!=0){
  		// 	int dx=lazy[si];
  		// 	if(ss!=se){
  		// 		lazy[2*si+1]+=dx;
  		// 		lazy[2*si+2]+=dx;
  		// 	}
  		// 	dx%=3;
  		// 	for(int i=0;i<dx;i++){
  		// 		int temp=seg[si].a;
  		// 		seg[si].a=seg[si].c;
  		// 		seg[si].c=seg[si].b;
  		// 		seg[si].b=temp;
  		// 	}
  		// 	lazy[si]=0;
  		// }
  		if(se<qs || ss>qe)return 0;
  		if(ss>=qs && se<=qe)
  		{
  			int u=upper_bound(seg[si],val+1,0,seg[si].size()-1);
  			if(u==-1)return 0;
  			else return seg[si].size()-u;
  		}
  		int mid=(ss+se)/2;
  		return query(2*si+1,ss,mid,qs,qe,val)+query(2*si+2,mid+1,se,qs,qe,val);
  	}
  	//Segment Tree Code end
  
  	public static HashSet<Long> primeFact(long a)
  	{
  	    HashSet<Long> arr=new HashSet<>();
  	    while(a%2==0){
  	        arr.add(2L);
  	        a=a/2;
  	    }
  	    for(long i=3;i*i<=a;i+=2){
  	        while(a%i==0){
  	            arr.add(i);
  	            a=a/i;
  	        }
  	    }
  	    if(a>2)arr.add(a);
  	    return arr;
  	}
  	public static boolean isInteger(double N)
  	{
  		int X = (int)N;
  		double temp2 = N - X;
  		if (temp2 > 0)
  		{
  			return false;
  		}
  		return true;
  	}
  	public static boolean isPalindrome(String s,int n)
  	{
  		for(int i=0;i<=n/2;i++){
  			if(s.charAt(i)!=s.charAt(n-i-1)){
  				return false;
  			}
  		}
  		return true;
  	}
  	public static int gcd(int a,int b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long gcd(long a,long b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long lcm(long a,long b){return (a*b)/gcd(a,b);}
  	public static long fact(long n)
  	{
  		long fact=1;
  		for(long i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	}
  	public static long fact(int n)
  	{
  		long fact=1;
  		for(int i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	} 
  	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; 
  	    double sq=Math.sqrt(n);
  	  
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	} 
      public static boolean isPrime(long n) 
  	{ 
  	    if (n <= 1) 
  	        return false; 
  	    if (n <= 3) 
  	        return true; 
  	    if (n % 2 == 0 || n % 3 == 0) 
  	        return false; 
  	    double sq=Math.sqrt(n);
  	
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	}
  	public static void printArray(long a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(int a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(char a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]);
  		}
  		out.println();
  	}
  	public static void printArray(String a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(boolean a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(pair a[])
  	{
  		for(pair p:a){
  			out.println(p.a+"->"+p.b);
  		}
  	}
  	public static void printArray(int a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(long a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(char a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArrayL(ArrayList<Long> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayI(ArrayList<Integer> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayS(ArrayList<String> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printMapInt(HashMap<Integer,Integer> hm){
  		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  	public static void printMapLong(HashMap<Long,Long> hm){
  		for(Map.Entry<Long,Long> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  
  	//Modular Arithmetic
  
  	public static long add(long a,long b)
  	{
  		a+=b;
  		if(a>=mod)a-=mod;
  		return a;
  	}
  	public static long sub(long a,long b)
  	{
  		a-=b;
  		if(a<0)a+=mod;
  		return a;
  	}
  	public static long mul(long a,long b)
  	{
  		return ((a%mod)*(b%mod))%mod;
  	}
  	public static long divide(long a,long b,long m)
  	{
  		a=mul(a,modInverse(b,m));
  		return a;
  	}
  	public static long modInverse(long a,long m)
  	{
  		int x=0,y=0;
  		own p=new own(x,y);
  		long g=gcdExt(a,m,p);
  		if(g!=1){
  			out.println("inverse does not exists");
  			return -1;
  		}else{
  			long res=((p.a%m)+m)%m;
  			return res;
  		}
  	}
  	public static long gcdExt(long a,long b,own p)
  	{
  		if(b==0){
  			p.a=1;
  			p.b=0;
  			return a;
  		}
  		int x1=0,y1=0;
  		own p1=new own(x1,y1);
  		long gcd=gcdExt(b,a%b,p1);
  		p.b=p1.a - (a/b) * p1.b;
  		p.a=p1.b;
  		return gcd;
  	}
  	public static long pwr(long m,long n)
  	{
  		long res=1;
  		if(m==0)
  		return 0;
  		while(n>0)
  		{
  			if((n&1)!=0)
  			{
  				res=(res*m);
  			}
  			n=n>>1;
  			m=(m*m);
  		}
  		return res;
  	}
  	public static long modpwr(long m,long n)
  	{
  		long res=1;
  		m=m%mod;
  		if(m==0)
  		return 0;
  		while(n>0)
  		{
  			if((n&1)!=0)
  			{
  				res=(res*m)%mod;
  			}
  			n=n>>1;
  			m=(m*m)%mod;
  		}
  		return res;
  	}
  	public static class own
      {
      	long a;
      	long b;
      	public own(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
  
  	//Modular Airthmetic
  
  	public static void sort(int[] A)
  	{
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              int tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
      }
  	public static void sort(char[] A)
  	{
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              char tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
      }
      public static void sort(long[] A)
  	{
  	    int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              long tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
  	    Arrays.sort(A);
  	}
  
  	//max & min
  	public static int max(int a,int b){return Math.max(a,b);}
  	public static int min(int a,int b){return Math.min(a,b);}
  	public static int max(int a,int b,int c){return Math.max(a,Math.max(b,c));}
  	public static int min(int a,int b,int c){return Math.min(a,Math.min(b,c));}
  	public static long max(long a,long b){return Math.max(a,b);}
  	public static long min(long a,long b){return Math.min(a,b);}
  	public static long max(long a,long b,long c){return Math.max(a,Math.max(b,c));}
  	public static long min(long a,long b,long c){return Math.min(a,Math.min(b,c));}
  	//end
  
  	public static int I()throws IOException{return sc.I();}
      public static long L()throws IOException{return sc.L();}
      public static String S()throws IOException{return sc.S();}
      public static double D()throws IOException{return sc.D();}
  }
  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 I(){ 
          return Integer.parseInt(next());
      }
      long L(){ 
          return Long.parseLong(next());
      }
      double D(){
           return Double.parseDouble(next());
      }
      String S(){
          String str = "";
          try 
          {
              str = br.readLine();
          }
          catch (IOException e)
          {
              e.printStackTrace();
          }
          return str;
      }
  }
  