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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.ArrayList;
import java.util.Collection;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Objects;

/**
 * @author ethan55
 */
public class Solution {
  public static void main(String[] args) {
    TestRunner.run();
  }

  public static class TestCase {
    static final boolean MULTIPLE = true;

    public void solve(InputReader in, OutputWriter out) {
      int[] nums = in.nextIntArray(in.nextInt());
      List<Integer> result = new ArrayList<>();
      result.add(0);
      for (int i = 1; i < nums.length; i++) {
        int r = 0;
        for (int j = 0; j < 32; j++) {
          boolean prevOne = (nums[i - 1] & (1 << j)) > 0;
          boolean currOne = (nums[i] & (1 << j)) > 0;
          if (prevOne && !currOne) {
            r |= (1 << j);
          }
        }
        result.add(r);
        nums[i] |= r;
      }
      out.println(result);
    }
  }

  public static class TestRunner {

    public static void run() {
      InputReader in = new InputReader(System.in);
      try (OutputWriter out = new OutputWriter(System.out)) {
        int testCases = TestCase.MULTIPLE ? in.nextInt() : 1;
        for (int i = 1; i <= testCases; i++) {
          new TestCase().solve(in, out);
        }
      }
    }

  }

  public static class InputReader {
    private final InputStream inputStream;
    private final byte[] inputBuffer = new byte[1024];
    private int bytesRead = 0;
    private int inputBufferIndex = 0;

    public InputReader(InputStream inputStream) {
      this.inputStream = inputStream;
    }

    private int readByte() {
      if (bytesRead == -1) {
        throw new InputMismatchException();
      }
      if (inputBufferIndex >= bytesRead) {
        inputBufferIndex = 0;
        try {
          bytesRead = inputStream.read(inputBuffer);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (bytesRead <= 0) {
          return -1;
        }
      }
      return inputBuffer[inputBufferIndex++];
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public long nextLong() {
      long num = 0;
      int b;
      boolean minus = false;
      do {
        b = readByte();
      } while (b != -1 && !((b >= '0' && b <= '9') || b == '-'));
      if (b == '-') {
        minus = true;
        b = readByte();
      }

      while (true) {
        if (b >= '0' && b <= '9') {
          num = num * 10 + (b - '0');
        } else {
          return minus ? -num : num;
        }
        b = readByte();
      }
    }

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

  }

  public static class OutputWriter implements AutoCloseable {
    private static final int BUFFER_SIZE = 1 << 13;
    private final byte[] outputBuffer = new byte[BUFFER_SIZE];
    private final OutputStream outputStream;
    private int outputBufferIndex = 0;

    public OutputWriter(OutputStream os) {
      this.outputStream = os;
    }

    public <T> OutputWriter println(Collection<T> c) {
      return writeln(c);
    }

    public void flush() {
      innerFlush();
      try {
        outputStream.flush();
      } catch (IOException e) {
        throw new IllegalStateException("Failed to flush");
      }
    }

    private OutputWriter write(byte b) {
      outputBuffer[outputBufferIndex++] = b;
      if (outputBufferIndex == BUFFER_SIZE) {
        innerFlush();
      }
      return this;
    }

    private OutputWriter write(char c) {
      return write((byte) c);
    }

    private OutputWriter write(String s) {
      s.chars()
          .forEach(
              c -> {
                outputBuffer[outputBufferIndex++] = (byte) c;
                if (outputBufferIndex == BUFFER_SIZE) {
                  innerFlush();
                }
              });
      return this;
    }

    private <T> OutputWriter writeln(Collection<T> c) {
      return write(c).writeln();
    }

    private <T> OutputWriter write(Collection<T> xs) {
      boolean first = true;
      for (T x : xs) {
        if (!first) {
          write(' ');
        }
        first = false;
        write(x);
      }
      return this;
    }

    private OutputWriter write(Object o) {
      return write(Objects.toString(o));
    }

    private OutputWriter writeln() {
      return write((byte) '\n');
    }

    private void innerFlush() {
      try {
        outputStream.write(outputBuffer, 0, outputBufferIndex);
        outputBufferIndex = 0;
      } catch (IOException e) {
        throw new IllegalStateException("Failed to inner flush");
      }
    }

    @Override
    public void close() {
      flush();
    }
  }
}