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 Test {
    static class Scan {
        private byte[] buf = new byte[1024];
        private int index;
        private InputStream in;
        private int total;

        public Scan() {
            in = System.in;
        }

        public int scan() throws IOException {
            if (total < 0)
                throw new InputMismatchException();
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0)
                    return -1;
            }
            return buf[index++];
        }

        public int scanInt() throws IOException {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            return neg * integer;
        }

        public long scanLong() throws IOException {
            long integer = 0;
            long n = scan();
            while (isWhiteSpace(n))
                n = scan();
            long neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            return neg * integer;
        }

        public double scanDouble() throws IOException {
            double doub = 0;
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n) && n != '.') {
                if (n >= '0' && n <= '9') {
                    doub *= 10;
                    doub += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            if (n == '.') {
                n = scan();
                double temp = 1;
                while (!isWhiteSpace(n)) {
                    if (n >= '0' && n <= '9') {
                        temp /= 10;
                        doub += (n - '0') * temp;
                        n = scan();
                    } else
                        throw new InputMismatchException();
                }
            }
            return doub * neg;
        }

        public String scanString() throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            while (!isWhiteSpace(n)) {
                sb.append((char) n);
                n = scan();
            }
            return sb.toString();
        }

        private boolean isWhiteSpace(long n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
                return true;
            return false;
        }
    }

    static class Print {
        private final BufferedWriter bw;

        public Print() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void print(Object object) throws IOException {
            bw.append("" + object);
        }

        public void println(Object object) throws IOException {
            print(object);
            bw.append("\n");
        }

        public void close() throws IOException {
            bw.close();
        }
    }

    public static void main(String[] args) throws IOException {
        Scan scan = new Scan();
        Print print = new Print();
        int testcases = scan.scanInt();
        while (testcases-- > 0) {
            int n = scan.scanInt();
            int a[] = new int[n];
            for(int i=0; i<n; i++)
                a[i] = scan.scanInt();
            int ans[] = new int[n];
            int array[] = new int[31];
            ans[0] = 0;
                int num = a[0];
                int count = 0;
                while(num>0){
                    if(num%2 == 1){
                        array[count] = 1;
                    }
                    count++;
                    num/=2;
                }
            
            for(int i=1; i<n; i++){
                int y = a[i];
                count = 0;
                num = 0;
                for(int j=0; j<31; j++){
                    
                    if(y%2 != 1 && array[count] == 1){
                        num += (int)Math.pow(2, count);
                    }
                    if(y%2 == 1)
                        array[count] = 1;
                    count++;
                    y /= 2;
                }
                ans[i] = num;
            }
            for(int i=0; i<n; i++){
                print.print(ans[i]+" ");
            }
            print.println("");
            

        }
        print.close();
    }

}
