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 
// Author : RegalBeast

import java.io.*;
import java.util.*;
import java.util.concurrent.*;

public class Main implements Runnable {
  static Input in = new Input();
  static PrintWriter out = Output();
  
  public static void main(String[] args) {
    new Thread(null, new Main(), String.join(
                                  "All that is gold does not glitter,",
                                  "Not all those who wander are lost;",
                                  "The old that is strong does not wither,",
                                  "Deep roots are not reached by the frost.",
                                  
                                  "From the ashes a fire shall be woken,",
                                  "A light from the shadows shall spring;",
                                  "Renewed shall be blade that was broken,",
                                  "The crownless again shall be king."
                                ), 1<<25).start();
  }

  public void run() {
    int tests = in.nextInt();
    for (int t = 0; t < tests; t++) {
      int n = in.nextInt();
      int[] x = new int[n];
      for (int i = 0; i < n; i++) {
        x[i] = in.nextInt();
      }

      int[] y = getY(x);
      for (var val : y) {
        out.print(val + " ");
      }
      out.println();
    }

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

  static int[] getY(int[] x) {
    int[] y = new int[x.length];
    boolean[] prev = new boolean[30];

    for (int i = 0; i < x.length; i++) {
      int num = 0;
      int bit = 1;
      for (int j = 0; j < 30; j++, bit<<=1) {
        if ((x[i] & bit) > 0) {
          prev[j] = true;
        } else {
          if (prev[j]) {
            num |= bit;
          }
        }
      }
      
      y[i] = num;
    }

    return y;
  }

  static PrintWriter Output() {
    return new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
  }
  
  static PrintWriter Output(String fileName) {
    PrintWriter pw = null;
    try {
      pw = new PrintWriter(new BufferedWriter(new FileWriter(fileName)));
    } catch (IOException ex) {
      ex.printStackTrace();
    }
    return pw;
  }
}

class Input {
  BufferedReader br;
  StringTokenizer st;
  public Input() {
    br = new BufferedReader(new InputStreamReader(System.in));
  }

  public Input(String fileName) {
    try {
      br = new BufferedReader(new FileReader(fileName));
    } catch (IOException ex) {
      ex.printStackTrace();
    }
  }

  public String next() {
    while (st == null || !st.hasMoreElements()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (IOException ex) {
        ex.printStackTrace();
      }
    }
    return st.nextToken();
  }

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

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

  public Float nextFloat() {
    return Float.parseFloat(next());
  }

  public Double nextDouble() {
    return Double.parseDouble(next());
  }

  public String nextLine() {
    if (st != null && st.hasMoreElements()) {
      StringBuilder sb = new StringBuilder();
      while (st.hasMoreElements()) {
        sb.append(next());
      }
      return sb.toString();
    }

    String str = null;
    try {
      str = br.readLine();
    } catch (IOException ex) {
      ex.printStackTrace();
    }
    return str;
  }

  public void close() {
    try {
      br.close();
    } catch (IOException ex) {
      ex.printStackTrace();
    }
  }
}