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 java.io.*;

public class D {

    public void prayGod() throws IOException {
        int t = nextInt();
        while (t-- > 0) {
            int n = nextInt();
            int[] x = nextIntArray(n);
            int[] y = new int[n];

            for (int i = 1; i < n; i++) {
                for (int j = 0; j < 30; j++) {
                    int prev = x[i - 1] & (1 << j), curr = x[i] & (1 << j);
                    if (prev != 0 && curr == 0)
                        y[i] |= 1 << j;
                }
                x[i] ^= y[i];
            }

            for (int val : y)
                out.printf("%d ", val);
            out.println();

        }
    }

    static final boolean RUN_TIMING = true;
    static final boolean AUTOFLUSH = false;
    static final boolean FILE_INPUT = false;
    static final boolean FILE_OUTPUT = false;

    static int iinf = 0x3f3f3f3f;
    static long inf = (long) 1e18 + 10;
    static long mod = 998244353L;

    static char[] inputBuffer = new char[1 << 20];
    static PushbackReader in = new PushbackReader(new BufferedReader(new InputStreamReader(System.in)), 1 << 20);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), AUTOFLUSH);

    // int data-type
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    public void sort(int[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

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

    // long data-type
    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

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

    public void sort(long[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    // double data-type
    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) throws IOException {
        double[] arr = new double[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextDouble();
        return arr;
    }

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

    // Generic type
    public <T> void sort(T[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    public static <T> void printArray(T[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    public String next() throws IOException {
        int len = 0;
        int c;
        do {
            c = in.read();
        } while (Character.isWhitespace(c) && c != -1);
        if (c == -1) {
            throw new NoSuchElementException("Reached EOF");
        }
        do {
            inputBuffer[len] = (char) c;
            len++;
            c = in.read();
        } while (!Character.isWhitespace(c) && c != -1);
        while (c != '\n' && Character.isWhitespace(c) && c != -1) {
            c = in.read();
        }
        if (c != -1 && c != '\n') {
            in.unread(c);
        }
        return new String(inputBuffer, 0, len);
    }

    public String nextLine() throws IOException {
        int len = 0;
        int c;
        while ((c = in.read()) != '\n' && c != -1) {
            if (c == '\r') {
                continue;
            }
            inputBuffer[len] = (char) c;
            len++;
        }
        return new String(inputBuffer, 0, len);
    }

    public boolean hasNext() throws IOException {
        String line = nextLine();
        if (line.isEmpty()) {
            return false;
        }
        in.unread('\n');
        in.unread(line.toCharArray());
        return true;
    }

    public void shuffle(int[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(long[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(Object[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            Object temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public static void main(String[] args) throws IOException {
        if (FILE_INPUT)
            in = new PushbackReader(new BufferedReader(new FileReader(new File("output.txt"))), 1 << 20);
        if (FILE_OUTPUT)
            out = new PrintWriter(new FileWriter(new File("output.txt")));

        long time = 0;
        time -= System.nanoTime();
        new D().prayGod();
        time += System.nanoTime();

        if (RUN_TIMING)
            System.err.printf("%.3f ms%n", time / 1000000.0);

        out.flush();
        in.close();
    }
}
