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.*;

public class Main{


    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        
        // Start writing your solution here. -------------------------------------
        /*
        int n      = sc.nextInt();        // read input as integer
        long k     = sc.nextLong();       // read input as long
        double d   = sc.nextDouble();     // read input as double
        char c = sc.next().charAt(0);     // read input as char
        String str = sc.next();           // read input as String
        String s   = sc.nextLine();       // read whole line as String
        out.println(result);              // print via PrintWriter
        */
        //------------------------------------------------------------------

        int test= sc.nextInt();

        while(test -- > 0){

            int n = sc.nextInt();
            long[] arr = new long[n];
            
            for(int i = 0 ; i < n ; i++){
                arr[i] = sc.nextLong();
            }

            Set<Integer> set =new HashSet<>();
            // int[] ones = new int[32];
            // int totalOnes = 0;
            // int onesIndex= 0;

            

            ArrayList<Integer> answer = new ArrayList<>();

            // long first = curr[0];

            // while(curr > 0){

            // }


            int l = set.size();
            for(int i = 0 ; i < n ; i++){

                // System.out.println(set);

                long num = 0;
                long curr = arr[i];

                int index = 1;
                    while(curr > 0){
                        if(curr%2 == 1){
                            if(!set.contains(index)){
                                set.add(index);
                            }else{
                                l--;
                            }
                        }else{
                            if(set.contains(index)){
                                num += Math.pow(2, index-1);
                                set.add(index); 
                                l--;  
                            }
                        }
                        curr = curr >> 1;
                        index++;
                    }
                   
                
                while(l != 0){
                    if(set.contains(index)){
                        num += Math.pow(2, index-1);
                        l--;
                    }
                    index++;
                }
               
                l = set.size();
                answer.add((int)num);
            }

            StringBuilder sb = new StringBuilder();
            for(int i = 0 ; i < answer.size() ; i++){
                if(i == answer.size() -1){
                    sb.append(answer.get(i));
                }else{
                    sb.append(answer.get(i) + " ");
                }
            }

            String random = sb.toString();
            out.println(random);

        }

        //------------------------------------------------------------------
        
        // Stop writing your solution here. -------------------------------------
        out.close();
    }

     
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
      
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
        public MyScanner() {
            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;
        }

    }
   //--------------------------------------------------------
}