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.*;

public class Main {

    /************************ SOLUTION STARTS HERE ************************/
    private static void solve() {
        int t = nextInt();
        while(t-- > 0) {
            int n = nextInt();
            long[] arr = nextLongArray(n);
            long[] res = new long[n];
            long[] xor = new long[n];
            res[0] = 0;
            xor[0] = arr[0];

            for(int i=1;i<n;i++) {
                long temp = arr[i]^xor[i-1];
                res[i] = xor[i-1] & temp;
                xor[i] = arr[i]^res[i];
            }

            for(int i=0;i<res.length;i++) {
                print(res[i] + (i == res.length - 1 ? "" : " "));
            }
            println("");
        }
    }

    /************************ SOLUTION ENDS HERE ************************/



    /************************ TEMPLATE STARTS HERE **********************/

    public static void main(String[] args) throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false);
        st = null;
        solve();
        reader.close();
        writer.close();
    }

    static BufferedReader  reader;
    static PrintWriter     writer;
    static StringTokenizer st;

    static String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                String line = reader.readLine();
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
        return st.nextToken();
    }

    static String nextLine() {
        String s = null;
        try {
            s = reader.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }

    static long nextLong() {
        return Long.parseLong(next());
    }

    static double nextDouble() {
        return Double.parseDouble(next());
    }

    static char nextChar() {
        return next().charAt(0);
    }

    static int[] nextIntArray(int n) {
        int[] a = new int[n];
        int i = 0;
        while (i < n) {
            a[i++] = nextInt();
        }
        return a;
    }

    static long[] nextLongArray(int n) {
        long[] a = new long[n];
        int i = 0;
        while (i < n) {
            a[i++] = nextLong();
        }
        return a;
    }

    static int[] nextIntArrayOneBased(int n) {
        int[] a = new int[n + 1];
        int i = 1;
        while (i <= n) {
            a[i++] = nextInt();
        }
        return a;
    }

    static long[] nextLongArrayOneBased(int n) {
        long[] a = new long[n + 1];
        int i = 1;
        while (i <= n) {
            a[i++] = nextLong();
        }
        return a;
    }

    static void print(Object o) {
        writer.print(o);
    }

    static void println(Object o) {
        writer.println(o);
    }

    static void printArr(int[] arr) {
        for(int i = 0 ; i < arr.length; i++)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    /************************ TEMPLATE ENDS HERE ************************/
}
