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 Solution{
    public static void toBinary(ArrayList<int[]> al, long n, ArrayList<Long> ans){
        int itr=0;
        int[] arr = new int[30];
        while(n!=0){
            arr[itr] = (int)n%2;
            n/=2;
            itr++;
        }
        al.add(arr);
        if(al.size()>1){
            int[] curr = al.get(al.size()-2).clone();
            int[] curr1 = al.get(al.size()-1).clone();
            int[] newArr = new int[30];
            itr=0;
            long q = ans.get(ans.size()-1);
            while(q!=0){
                newArr[itr] = (int)q%2;
                q/=2;
                itr++;
            }
            long num=0;
            for(int i=0; i<30; i++){
                newArr[i] = curr[i]^newArr[i];
            }
            for(int i=0; i<30; i++){
                if(newArr[i]==1 && curr1[i]==0){
                    num+=Math.pow(2,i);
                }
            }
            ans.add(num);
        }else{
            ans.add((long)0);
        }
    }
    public static void main (String[] args) throws java.lang.Exception {
        FastReader sc = new FastReader();
        BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
        int testCase = sc.nextInt();
        while (testCase-->0){
            int n = sc.nextInt();
            long[] intArr = new long[n];
            ArrayList<int[]> al = new ArrayList<>();
            ArrayList<Long> ans=  new ArrayList<>();
            for(int i=0; i<n; i++){
                intArr[i] = sc.nextLong();
                toBinary(al, intArr[i], ans);
            }
            for(long aa:ans){
                output.write(aa+" ");
            }
            output.write("\n");
            output.flush();

        }
    }
    // Fast Reader Class
    static class FastReader {
        BufferedReader br; StringTokenizer st;
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } }return st.nextToken(); }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine() { String str = ""; try { str = br.readLine(); }  catch (IOException e) { e.printStackTrace(); }return str; }
    }
}