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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.lang.*;
public class JaiShreeRam{
	static Scanner in=new Scanner();
	static long mod = 1000000007;
	static int seive[]=new int[1000001];
	static int level[]=new int[200001];
	static int parent[][]=new int[200001][18];
	static ArrayList<ArrayList<Integer>> al=new ArrayList<>();
	static char s[];
	public static void main(String[] args) throws Exception{
		int t=in.readInt();
		while(t-->0) {
			/*int xa=in.readInt();
			int ya=in.readInt();
			int xb=in.readInt();
			int yb=in.readInt();
			int xf=in.readInt();
			int yf=in.readInt();*/
			int n=in.readInt();
			int a[]=nextIntArray(n);
			int b[]=new int[n];
			for(int i=1;i<n;i++) {
				int x=a[i]&a[i-1];
				if(x==a[i-1]) {
					b[i]=0;
					continue;
				}
				else {
					int z=count(a[i-1],a[i]);
					a[i]+=z;
					b[i]=z;
				}
			}
			for(int i=0;i<n;i++) {
				System.out.print(b[i]+" ");
			}
			System.out.println();
			
		}
	}
	static int count(int a,int b) {
		int c=0;
		int no=0;
		while(a!=0) {
			int ra=a%2;
			int rb=b%2;
			if(ra==1&&rb==0) {
				no+=Math.pow(2,c);
			}
			c++;
			a>>=1;
			b>>=1;
		}
		return no;
	}
	static void seive() {
		Arrays.fill(seive, 1);
		seive[0]=0;
		seive[1]=0;
		for(int i=2;i*i<1000001;i++) {
			if(seive[i]==1) {
				for(int j=i*i;j<1000001;j+=i) {
					if(seive[j]==1) {
						seive[j]=0;
					}
				}
			}
		}
	}
	static int[] nextIntArray(int n){
		int[] arr= new int[n];
		int i=0;
		while(i<n){
			arr[i++]=in.readInt();
		}
		return arr;
	}
	static int[] nextIntArray1(int n){
		int[] arr= new int[n+1];
		int i=1;
		while(i<=n){
			arr[i++]=in.readInt();
		}
		return arr;
	}
	static long gcd(long a, long b) {
		if (b==0) return a;
		return gcd(b, a%b);
	}
 
	static void ruffleSort(long[] a) {
		int n=a.length;
		Random r=new Random();
		for (int i=0; i<a.length; i++) {
			int oi=r.nextInt(n); long temp=a[i];
			a[i]=a[oi];
			a[oi]=temp;
		}
		Arrays.sort(a);
	}
	
	static class Scanner{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String readString() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		double readDouble() {
			return Double.parseDouble(readString());
		}
		int readInt() {
			return Integer.parseInt(readString());
		}
		long readLong() {
			return Long.parseLong(readString());
		}
	}	
}