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.StringTokenizer;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.io.IOException;
import java.io.BufferedReader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Collections;
import java.util.ArrayList;
import java.io.*;

public class p4
{
	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()); }

		byte nextByte() { return Byte.parseByte(next()); }

		short nextShort() { return Short.parseShort(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 void main(String[] args)throws Exception
	{
		FastReader fr=new FastReader();
		BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));

		short t=fr.nextShort();
		while(t-->0)
		{
			int n=fr.nextInt();
			int x[]=new int[n];
			for(int i=-1;++i<n;)
				x[i]=fr.nextInt();

			//System.out.print("0 ");
			int y[]=new int [n];
			for(int i=0;++i<n;)
			{
				y[i]=x[i-1]&(-1*x[i]-1);
				//System.out.print(y+" ");
				x[i]=x[i]^y[i];
			}
			for(int i=-1;++i<n;)
				System.out.print(y[i]+" ");
			System.out.println();
		}
	}
}