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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.nio.DoubleBuffer;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args) throws Exception {
    Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
    thread.start();
    thread.join();
  }

  static class TaskAdapter implements Runnable {
    @Override
    public void run() {
      InputStream inputStream = System.in;
      OutputStream outputStream = System.out;
      FastReader in = new FastReader(inputStream);
      PrintWriter out = new PrintWriter(outputStream);
      Solution solver = new Solution();
      int testCount = Integer.parseInt(in.next());
      for (int i = 1; i <= testCount; i++)
        solver.solve(1, in, out);
      out.close();
    }
  }

  static class Solution {
    public void solve(int testNumber, FastReader sc, PrintWriter w) {
      int n = sc.nextInt();
      long cur = 0;
      for (int i = 0 ; i < n ; i++) {
        long x = sc.nextLong();
        cur |= x;
        w.print((cur ^ x) + " ");
      }
      w.println();
    }
    private int gcd(int a, int b) {
      return b == 0 ? a : gcd(b, a % b);
    }
  }

  static class FastReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private FastReader.SpaceCharFilter filter;

    public FastReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {

      if (numChars == -1)
        throw new InputMismatchException();

      if (curChar >= numChars) {

        curChar = 0;

        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }

        if (numChars <= 0)
          return -1;
      }

      return buf[curChar++];
    }

    public int nextInt() {
      int c = read();

      while (isSpaceChar(c))
        c = read();

      int sgn = 1;

      if (c == '-') {
        sgn = -1;
        c = read();
      }

      int res = 0;
      do {
        if (c < '0' || c > '9')
          throw new InputMismatchException();
        res *= 10;
        res += c - '0';
        c = read();
      }
      while (!isSpaceChar(c));

      return res * sgn;
    }

    public long nextLong() {

      int c = read();

      while (isSpaceChar(c))
        c = read();

      int sgn = 1;

      if (c == '-') {
        sgn = -1;
        c = read();
      }

      long res = 0;

      do {
        if (c < '0' || c > '9')
          throw new InputMismatchException();

        res *= 10;
        res += c - '0';
        c = read();
      }

      while (!isSpaceChar(c));
      return res * sgn;
    }

    public String next() {

      int c = read();

      while (isSpaceChar(c))
        c = read();

      StringBuilder res = new StringBuilder();

      do {
        res.appendCodePoint(c);
        c = read();
      }
      while (!isSpaceChar(c));

      return res.toString();
    }

    public boolean isSpaceChar(int c) {

      if (filter != null)
        return filter.isSpaceChar(c);

      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);

    }

  }
}