A sequence of non-negative integers a_1, a_2, ..., a_n is called growing if for all i from 1 to n - 1 all ones (of binary representation) in a_i are in the places of ones (of binary representation) in a_{i + 1} (in other words, a_i \:\&\: a_{i + 1} = a_i, where \& denotes [bitwise AND](http://tiny.cc/xpy9uz)). If n = 1 then the sequence is considered growing as well.

For example, the following four sequences are growing: 

  * [2, 3, 15, 175] — in binary it's [10_2, 11_2, 1111_2, 10101111_2]; 
  * [5] — in binary it's [101_2]; 
  * [1, 3, 7, 15] — in binary it's [1_2, 11_2, 111_2, 1111_2]; 
  * [0, 0, 0] — in binary it's [0_2, 0_2, 0_2]. 



The following three sequences are non-growing: 

  * [3, 4, 5] — in binary it's [11_2, 100_2, 101_2]; 
  * [5, 4, 3] — in binary it's [101_2, 100_2, 011_2]; 
  * [1, 2, 4, 8] — in binary it's [0001_2, 0010_2, 0100_2, 1000_2]. 



Consider two sequences of non-negative integers x_1, x_2, ..., x_n and y_1, y_2, ..., y_n. Let's call this pair of sequences co-growing if the sequence x_1 ⊕ y_1, x_2 ⊕ y_2, ..., x_n ⊕ y_n is growing where ⊕ denotes [bitwise XOR](http://tiny.cc/bry9uz).

You are given a sequence of integers x_1, x_2, ..., x_n. Find the lexicographically minimal sequence y_1, y_2, ..., y_n such that sequences x_i and y_i are co-growing.

The sequence a_1, a_2, ..., a_n is lexicographically smaller than the sequence b_1, b_2, ..., b_n if there exists 1 ≤ k ≤ n such that a_i = b_i for any 1 ≤ i < k but a_k < b_k.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — length of the sequence x_i.

The second line contains n integers x_1, x_2, ..., x_n (0 ≤ x_i < 2^{30}) — elements of the sequence x_i.

It is guaranteed that the sum of n overall all test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print n integers y_1, y_2, ..., y_n (0 ≤ y_i < 2^{30}) — lexicographically minimal sequence such that such that it's co-growing with given sequence x_i.

Example

Input


5
4
1 3 7 15
4
1 2 4 8
5
1 2 3 4 5
4
11 13 15 1
1
0


Output


0 0 0 0 
0 1 3 7 
0 1 0 3 2 
0 2 0 14 
0 

import java.util.*;
 

import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class final2
{
	static class Pair{
    	int a;
    	int b;
    	
    }
    static 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 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; 
        } 
    } 
	public static int gcd(int a, int b)
	{
		if (b == 0)
	        return a;
	    return gcd(b, a % b);
	}
	static int findGCD(int arr[], int n)
    {
        int result = 0;
        for (int element: arr){
            result = gcd(result, element);
 
            if(result == 1)
            {
               return 1;
            }
        }
 
        return result;
    }
	public static void main (String[] args) throws java.lang.Exception


    {
		 /*Arrays.sort(time,new Comparator<Pair>(){
 			public int compare(Pair p1,Pair p2){
 				if(p1.a==p2.a)
 					return p1.b-p2.b;
 				return p1.a-p2.a;
 			}
 		});*/
	    
			//Your Solve
		FastReader sc = new FastReader();

        int t=sc.nextInt();
        PrintWriter out=new PrintWriter(System.out);
        
        Set<String> st1=new HashSet<String>();
        int i,j,a,b=4,c,d,k,l,r;
        
        long count=0;
        int m,n;
        long sum1=1,sum=0;
        long min,max,y,z;
        long x=0;
        int pos=1;  
        String s="",s1="";
        //ArrayList<Integer> arr2=new ArrayList<Integer>();
        //ArrayList<Integer> arr1=new ArrayList<Integer>();
        
        Map<Character,Integer> hm=new HashMap<Character,Integer>();
        //int arr[]=new int [32];
        for(;t>0;t--) 
        {
        	n=sc.nextInt();
        	int arr[]=new int[n];
        	for(i=0;i<n;i++)
        	{
        		arr[i]=sc.nextInt();
        		if(i==0)
        			out.print("0 ");
        		else
        		{
        			d=arr[i]^arr[i-1];
        			
        			d=d&arr[i-1];
        			out.print(d+" ");
        			arr[i]=arr[i]^d;
        		}
        	}
        	out.println();
        	
        }
        	
        
        out.close();
        
    
        
		
        
        
    }
}