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.*;
import java.math.BigInteger;

 public class Main {
    static long[] MODS = {1000000007L, 998244353L, 1000000009L};
    static long mod = MODS[0];

    public static void main(String[] args) {
        sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        	while(t-- >0) {
		  int num=sc.nextInt();
		  int[] arr=sc.nextArray(num);
		  int[] res=new int[num];
		  res[0]=0;
		  int mask=arr[0];
		  for(int i = 1; i < num; i++) {
		       int cur = 0;
		       for(long j = 0; j < 30; j++) {
		            if((mask & (1 << j)) != 0) {
		                 if(!((arr[i] & (1 << j)) != 0)) {
		                     cur += 1 << j;
		                 }
		            }
		       }
		       res[i] = cur; mask = arr[i] ^ res[i];
		   }
		  
		   for(int i=0;i<res.length;i++)
			   System.out.print(res[i]+" ");
		   
		   System.out.println();
		       
        	}
        	
        out.close();
    }

   
    //static 
    

	/*-----------------------------*/
    public static long[] sort(long[] arr) {
        ArrayList<Long> list = new ArrayList<>();
        for (int i = 0; i < arr.length; i++) {
            list.add(arr[i]);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
        return arr;
    }
    
    int sqDecom(int[] a,int l,int r) {
		int n=a.length;
		int len=(int)Math.ceil(Math.sqrt(n));
		int[] b=new int[len];
		for(int i=0;i<a.length;i++) {
			b[i/len]+=a[i];
		}
		
		int sum=0;
		int cl=l/len,cr=r/len;
		if(cl==cr) {
			for(int i=l;i<=r;i++) sum+=a[i];
		}else {
			for(int i=l;i<=(cl+1)*len-1;i++) {
				sum+=a[i];
			}
			for(int i=cl+1;i<=cr-1;i++) {
				sum+=b[i];
			}
			for(int i=cr*len;i<=r;i++) {
				sum+=a[i];
			}
		}
		return sum;
		
		
	}
    
    BigInteger gcd(BigInteger a,BigInteger b) {
		if(a.equals(new BigInteger("0")))return b;
		if(b.equals(new BigInteger("0")))return a;
		
		if(a.mod(new BigInteger("2")).equals(new BigInteger("0"))&&b.mod(new BigInteger("2")).equals(new BigInteger("0")))return gcd(a.divide(new BigInteger("2")),b.divide(new BigInteger("2"))).multiply(new BigInteger("2"));
		else if(a.mod(new BigInteger("2")).equals(new BigInteger("0"))&&b.mod(new BigInteger("2")).equals(new BigInteger("1")))return gcd(a.divide(new BigInteger("2")),b);
		else if(a.mod(new BigInteger("2")).equals(new BigInteger("1"))&&b.mod(new BigInteger("2")).equals(new BigInteger("0")))return gcd(a,b.divide(new BigInteger("2")));
		return gcd(b,b.subtract(a).abs());
		
	}

    public static void scan(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public static MyScanner sc;
    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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());
        }

        int[] nextArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = sc.nextInt();
			}
			return a;
		}
     			
       long[] nextLongArray(long n) {
			long[] a = new long[(int)n];
			for (int i = 0; i < n; i++) {
				a[i] = sc.nextLong();
			}
			return a;
		}
        
        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;
        }
    }
}

