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 
// HOPE

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///////            RRRRRRRRRRRRR     YY          YY         AA               NN         NN                    //////////
///////            RR         RR      YY        YY        AA  AA             NN NN      NN                    //////////
///////            RR        RR         YY     YY        AA    AA            NN  NN     NN                    //////////
///////            RRRRRRRRRR            YY   YY       AAAAAAAAAAAA          NN    NN   NN                    //////////
///////            RR RR                   YY         AAAAAAAAAAAAAA         NN      NN NN                    //////////
///////            RR   RR                 YY        AA            AA        NN       NNNN                    //////////
///////            RR     RR               YY       AA              AA       NN         NN                    //////////
///////            RR       RR_____________________________________________________________________________   //////////
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import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;

public class Codeforces {
    static final int mod=1_000_000_007;

    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;
        }
    }

    static final int N = (int) (1e5+10);
    public static void main(String[] args) {
        FastReader s = new FastReader();
        int t = s.nextInt();
        while (t-- > 0)
        {
            int n = s.nextInt();
            int[] x = new int[n];

            for(int i=0;i<n;i++)
            {
                x[i] = s.nextInt();
            }
            find(n, x);
        }
    }
    public static void find(int n, int[] x)
    {
        List<Integer> ls = new ArrayList<>();
        ls.add(0);

       for(int i=1;i<n;i++)
       {
          int prev = x[i-1] ^ ls.get(i-1);
          int curr = x[i];
          int sum = 0;

          for(int j=0;j<30;j++)
          {
              int set1 = (1<<j) & prev;
              int set2 = (1<<j) & curr;

              if(set1>0 && set2==0)
                  sum|=(1<<j);
          }
          ls.add(sum);
       }

       for(Integer y:ls)
           System.out.print(y+" ");

       System.out.println();

    }












    /////////////////////////////////////////////////THE END///////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////

    public static int gcd(int x,int y)
    {
        return y==0?x:gcd(y,x%y);
    }
    public static long gcd(long x,long y)
    {
        return y==0L?x:gcd(y,x%y);
    }

    public static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    public static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    public static long pow(long a,long b)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1)
                tmp*=a;
            a*=a;
            b>>=1;
        }
        return (tmp*a);
    }

    public static long modPow(long a,long b,long mod)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1L)
                tmp*=a;

            a*=a;
            a%=mod;
            tmp%=mod;
            b>>=1;
        }
        return (tmp*a)%mod;
    }

    static long mul(long a, long b) {
        return a*b%mod;
    }

    static long fact(int n) {
        long ans=1;
        for (int i=2; i<=n; i++) ans=mul(ans, i);
        return ans;
    }

    static long fastPow(long base, long exp) {
        if (exp==0) return 1;
        long half=fastPow(base, exp/2);
        if (exp%2==0) return mul(half, half);
        return mul(half, mul(half, base));
    }


    static boolean check(int n,int d)//check for digit 7 in 504732 number
    {
        String s = n+"";
        return s.contains(d + "");
    }
    static void reverseArray(int[] a) {
        int n = a.length;
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static void reverseArray(long[] a) {
        int n = a.length;
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static class Pair{
        int x, y;
        Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }
}
