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 
//package com.amoghghadge.compProgramming.Codeforces1000To1300;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class CoGrowingSequences {
    
    public static void main(String[] args) {
        
        FastReader in = new FastReader();
        StringBuffer sb = new StringBuffer();

        int t = in.nextInt();

        while (t > 0) {

            int n = in.nextInt();
            ArrayList<Integer> x = new ArrayList<Integer>();
            ArrayList<Integer> y = new ArrayList<Integer>();

            for (int i = 0; i < n; i++) {

                x.add(in.nextInt());

            }

            y.add(0);

            for (int i = 1; i < n; i++) {

                int prevXor = x.get(i - 1) ^ y.get(i - 1);
                int now = x.get(i);

                // By doing ~ you get the bitwise opposite, so the xor (^) of the two numbers would just be infinite 1s
                // By using the & bitwise operator with the previous xor, you restrict how big the new xor would be, so that
                // it becomes a positive number that is at least as big as the previous xor'd number (making it growing)
                int turnedOff = prevXor & ~now;
                y.add(turnedOff);

            }

            for (int z : y) {

                sb.append(z + " ");

            }

            sb.append("\n");

            t--;

        }

        in.println(sb);
        in.close();

    }

    static int gcd (int a, int b) {
        
        if (b == 0) {

            return a;

        } else {

            return gcd(b, a % b);

        }

    }
 
    static long gcd (long a, long b) {
        
        if (b == 0) {

            return a;

        } else {

            return gcd(b, a % b);

        }

    }
 
    static long lcm (int a, int b) {

        return (long) a / gcd(a, b) * b;

    }
 
    static long lcm (long a, long b) {

        return a / gcd(a, b) * b;

    }

    public static int search (int l, int r, int[] a, int key) {

        while (l <= r) {

            int middle = ((r - l) / 2) + l;

            if (a[middle] == key) {

                return middle;

            } else if (a[middle] < key) {

                l = middle + 1;

            } else {

                r = middle - 1;

            }

        }

        return -1;

    }

    public static void sort (int[] a) {

		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
        
	}

    public static void sort (long[] a) {

		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);

	}

    static class FastReader extends PrintWriter {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {

            this(System.in, System.out); 
            
        }

		public FastReader(InputStream i, OutputStream o) {

			super(o);
			br = new BufferedReader(new InputStreamReader(i));

		}

        public FastReader(String problemName) throws IOException {

			super(new FileWriter(problemName + ".out"));
			br = new BufferedReader(new FileReader(problemName + ".in"));

		}

        public String next() {

            while (st == null || !st.hasMoreElements()) {

                try {

                    st = new StringTokenizer(br.readLine());

                } catch (IOException e) {

                    e.printStackTrace();

                }

            }

            return st.nextToken();

        }

        public int nextInt() {

            return Integer.parseInt(next());

        }

        public long nextLong() {

            return Long.parseLong(next());

        }

        public double nextDouble() {

            return Double.parseDouble(next());

        }

        public String nextLine() {

            String str = "";

            try {

                str = br.readLine();

            } catch (IOException e) {

                e.printStackTrace();

            }

            return str;

        }

        public int[] readArray(int n) {

			int[] a = new int[n];

			for (int i = 0; i < n; i++) {
                
                a[i] = nextInt();
			
            }

            return a;

		}

        public long[] readArrayLong(long n) {

			long[] a = new long[(int) n];

			for (int i = 0; i < n; i++) {
                
                a[i] = nextLong();
			
            }

            return a;

		}

    }

}
