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 
import java.lang.Math;
public class solution {
	
	static int mod=1000000007;
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int testcases = s.nextInt();
		while(testcases-->0) {
		
			
			 int n=s.nextInt();
		      
		      ArrayList<Integer> x=new ArrayList<>(n);
		      for (int i = 0; i < n; i++) {
		      x.add(s.nextInt());
		      
		      }
		      int[] y=new int[n];
	
		      y[0] = 0;
		      int hello=0;
		      int raq=x.get(0);
		      for (int i = 1; i < n; i++) {
		         for (int j = 0; j <= 31; j++) {
		        	   if (((raq >> j) & 1)==1 && ((x.get(i) >> j) & 1)==0) {
		                   y[i] += (1 << j);
		                   hello++;
		                } else if (((raq >> j) & 1)==0 && ((x.get(i) >> j) & 1)==1) {
		                   raq += (1 << j);
		                   hello--;
		                }
		         }
		         hello-=hello;
		      }
		      for (int i = 0; i < n; i++) {
		    	  System.out.print(y[i]+" ");
		      }
		      System.out.println();
			
			
			
		}		
//		}
	}
	
	
	
	static long pow(long x, long y)
	{
	    long temp;
	    if( y == 0)
	        return 1;
	    temp = pow(x, y / 2);
	    if (y % 2 == 0) {
	    	temp=(temp*temp);
	        return temp;
	    }
	    else {
	    	temp=(temp*temp);
	    	temp=(temp*x);
	        return temp;
	    }
	}
	
	static long cl(long a, long x) {return a % x == 0 ? a / x : a / x + 1;}
	
	 
  

	
	
}



