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 
#----------FASTIOSTART-----------#
from __future__ import division, print_function
import os
import sys
from io import BytesIO, IOBase
if sys.version_info[0] < 3:
	from __builtin__ import xrange as range
	from future_builtins import ascii, filter, hex, map, oct, zip
BUFSIZE = 8192
class FastIO(IOBase):
	newlines = 0
	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = "x" in file.mode or "r" not in file.mode
		self.write = self.buffer.write if self.writable else None
	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines = 0
		return self.buffer.read()
	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b"\n") + (not b)
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines -= 1
		return self.buffer.readline()
	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode("ascii"))
		self.read = lambda: self.buffer.read().decode("ascii")
		self.readline = lambda: self.buffer.readline().decode("ascii")
def print(*args, **kwargs):
	sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
	at_start = True
	for x in args:
		if not at_start:
			file.write(sep)
		file.write(str(x))
		at_start = False
	file.write(kwargs.pop("end", "\n"))
	if kwargs.pop("flush", False):
		file.flush()
if sys.version_info[0] < 3:
	sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
	sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#----------FASTIOFINISH----------#
import collections,string,bisect,re,random,queue,itertools,statistics,math
from collections import *
from bisect import *
from string import *
from itertools import * 
from statistics import *
from math import *
from re import *
from queue import *
#----------SASTA_STL-------------#
# stack
class Stack:
    def __init__(self):self.items = []
    def push(self, item):self.items.append(item)
    def pop(self):return self.items.pop()
    def empty(self):return self.items == []
    def size(self):return len(self.items)
    def at(self,idx):
    	try:return self.items[idx]
    	except:return -1
#priority_queue
class priority_queue(object):
    def __init__(self):self.queue = []
    def __str__(self):return ' '.join([str(i) for i in self.queue])
    def empty(self):return len(self.queue) == 0
    def push(self, data):self.queue.append(data)
    def pop(self):
        try:
            max = 0
            for i in range(len(self.queue)):
                if self.queue[i] > self.queue[max]:
                    max = i
            item = self.queue[max]
            del self.queue[max]
            return item
        except IndexError:
            print()
            exit()
#----------SASTA_STL-------------#
mod  = int(1e9+7)
imax = float("inf")
imin = float("-inf")
true = True
false= False
N 	 = int(1e5)
none = None
inp  = lambda : input()
I    = lambda : int(inp())
M    = lambda : map(int,inp().split())
MS   = lambda : map(str,inp().split())
S    = lambda : list(MS())
L    = lambda : list(M())
def IO():
	try:
		sys.stdin = open('input.txt', 'r');
		sys.stdout = open('uttar.txt', 'w')
	except:
		pass
IO()
class helper:
	def first(self,arr):
		return arr[0]
	def second(self,arr):
		return arr[1]
	def is_sorted(self,arr):
		return arr==sorted(arr)

#----------TOTKA---------#

def kabraji_ka_totka():
	# totka hai dosto !
	n=I()
	arr=L()
	temp=0
	for i in arr:
		temp|=i;
		print(temp^i)

#----------TOTKA----------#
if __name__ == '__main__':
	case=1;
	case=I()
	for i in range(case):
		kabraji_ka_totka()
