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 
///package MyPackage;
import java.io.*;
import java.util.*;
public class MyClass {
    final static long mod = 1_000_000_007;
    final static int mini = Integer.MIN_VALUE;
    final static int maxi = Integer.MAX_VALUE;
    static long gcd(long a, long b) {
        if (b==0) return a;
        return gcd(b,a%b);
    }
    static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static long digits(long n) {
        long count = 0;
        long temp = n;
        while(temp > 0) {
            temp /= 10;
            count++;
        }
        return count;
    }
    private static boolean isPalindrome(long i) {
        long originalNum = i;
        long remainder;
        long reversedNum = 0;
        while (i != 0) {
            remainder = i % 10;
            reversedNum = reversedNum * 10 + remainder;
            i /= 10;
        }
        return originalNum == reversedNum;
    }
    static long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }
    static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static void reverse(int[] arr) {
        int l = 0;
        int h = arr.length - 1;
        while(l < h) {
            swap(arr, l, h);
            l++;
            h--;
        }
    }
    static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String n() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nint() {
            return Integer.parseInt(n());
        }
        float nfloat() {
            return Float.parseFloat(n());
        }
        long nlong() {
            return Long.parseLong(n());
        }
        double ndouble() {
            return Double.parseDouble(n());
        }
        String nline() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static class Pair {
        int a;
        int b;
        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
    }
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = sc.nint();
        while(t-- > 0) {
            int n = sc.nint();
            int[] arr = new int[n];
            for(int i = 0; i < n; i++) arr[i] = sc.nint();
            int[] res = new int[n];
            for(int i = 1; i < n; i++) {
                int prev = arr[i - 1] ^ res[i - 1];
                int x = arr[i];
                int off = prev & ~x;
                res[i] = off;
            }
            for(int i = 0; i < n; i++) {
                out.print(res[i] + " ");
            }
            out.println();
        }
        out.flush();
        out.close();
    }
}