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 
"""RANK1ZEN; 3966 PEAK; NA; FLEX SUPPORT: Zen, Bap; Battlenet ID -> Knuckles#11791"""
# region ---------------------------------------------------------------------------|
# MNNNNNNNNNNNNNNNNMNho///++//+oooooossssssssssssysssooyyyyyso+//++//shNNNNNNNNNNNNNM
# MNNNNNNNNNNNNNNMNy////////++++oooooooooossssssssoosssssysyyysoossss+/oshNNNNNNNNNNM
# MNNNNNNNNNNNNMNs///////+oooooo++++oooooooooooso+ossssssssssssssssssss++soymMNNNNNNM
# MNNNNNNNNNNNMd/:-//+//shNNmhsoo+++++++++ooooo++oooooooooossssssssssssso+ooosmNNNNNM
# MNNNNNNNNNNMh::://+/+ymMMMMmhsoso+++++++++o+/+ooooooooooooooooooooossso++o+++hMNNNM
# MNNNNNNNNNMy//-:/+/osmMMMMNhssyshNdssoooo++:++++++++++oooooooooooooooooo++-++/sMMNM
# MNNNNNNNNMd:/:///+/ohNMMMNhsohyyNMNNNdhhs+:++++++++++++++++++++ooooooooo/+.o+:/+NNM
# MNNNNNNNMm/:/-///++ooshmmhs+sysdMMMMNdMMd/+++++ooo++++++++++++++++++++++::-++/:/sNM
# MNNNNNNMN/://-+++++++++oo+//yosNMNMNmNMNo/o/oshNmhyoo+++++++++++++++++++/-/+++:/:sM
# MNNNNNMNo://-/+++++:/+++++//++osyhmdhMNs/o/+shMMMMmsooooyo++/+++++++++++://+++://oM
# MNNNNNMs:///:/++++//++-/+/:++++++ooooyo++o-oyNNMMmysooymmso/+shysyyysooo+/++o+/-s+M
# MNNNNMd:///+:/++++-++:`++:/++++//++++++:+-/oyhsmys+oohmyo++:sNMdmMMNNysy+-ohNs+-myM
# MNNNMN::///+-:+++:.+/``++/++++++++++++:+/`+++oo/:/++oyo+oy+odNddMMMMmyyh:-sdMh/odyN
# MNNNNo:///++-:+o/`::```++/+++++++++++//+-.o++:-:/++/+/+ymo/+ossyyhdhssy+.:ohhd/sy+M
# MMNMh-///+++--oo:`/````++-+++++++++++-o/`/+:.:/+++//+hmNo/++++++ooooooo-`/+o++/++-M
# MMMN/:///+++-.o/````-s:+/:++++++++++/++`.:.-/++++/+sdmmo/+++++++++++++: -+++++////M
# MMMh:///++++-`+:```/dN+/::++++++++++++:``.+ooo++ohNMNm++oooooooo+++++o+ :++++/-//oM
# MMd:/-/+++++-`/.``:hmm//./+++++++++o/o..:osoooymmdddmoooooooooooooo+oms.+++++////+M
# MMo// -+++++:`.`` dNddo-.:+++++++++++--/soo:.--::ymh+ssssssssssooo+sNN/++++++++/-dM
# Md/// `/+++o/```` dMddN.-:++++++++++/`/o/+:``-:-`/ooyssssssssssssoodmMo++++++++//NM
# M/:// `-+oooo.``` oMNMM+--/+++++++++/:yd-``.`-+o+hoyyoosyyyyyyys:+o+o++o//+++++/hMM
# m++:/```:oooo/````.dmNNm/-/+++++++//+dhy::ohs:/hysyosyyyyyyyyys:----:-/o/ooo++/-mMM
# s:++//```/oooo-  ``yNmdm:-/++++++////MMNmdhoys+ssssyyyyyysoysss:-.odd/o+/+oo++-+MMM
# s`:++/````:oooo. ```:hNNh-/++++++//:hNNNMMNMdsossyyyyyyss+osdM/o/:yNyoo///ooo/.MMNM
# d `-++/-```:+oo+-`````-+ds/++++++//-mMMMNNhs+syyysysyys+osdMMNyoshdh/+/o:ooo+.+MMNM
# M/` `-/+/-``.:ooo-```````s:++++++++/mNdhsoossssyyhyo/-+hmMMMMNNNNNNo//+.:oo++ oMMNM
# MMo``:..-//-.`-+oo:.`````/+++++++++:ooossyhyyyo+:-:ohNMmMMMMMNmNNNh:/:` :oo/: mMMNM
# MMMh.oMh+``.-:-.-/o+-````mh/+++++++:++++/:--:+syhmMMMMMNMMMMMMMMMo-.//``+oo:`-MMNNM
# MMMMh-omNd+````..`./+/.`hMMs+++++++/dmmmmNMMNNMMMMMMMMMMMMMMMMms:`` :/..+oo: yMNNNM
# MNNNMN/``..``````````.-.+dNy-oooooo/o+s++sNMMNmNMMmmNMMMMMMMmo-   ``-/.-oo+- yMNNNM
# MNNNNMMNdy-``````..``````-+o/+ooooo/++///:`:yMMMMMMMMMMMMds/`/++/````o--o++- MMNNNM
# MMNNMMMMMN:`........-:+oyssoo+ssssss:ooo+/+:`:mMMMMMNho/.````+ooohd+//:+ooo-/MMMMMM
# MMMMMMMMMMs.-...-.-osyyyyysdMhshhhhhossssssdh-.ss+/-.``----.sdhy+mMMMsosssy:sMMMMMM
# endregion ------------------------------------------------------------------------|
# region ---------------------------------------------------------------------------|
from sys import stdin
from bisect import bisect_left, bisect_right, insort_left, insort_right
from math import sqrt, ceil, floor
from collections import Counter, deque
from heapq import heappush, heappop, heapify
input = stdin.readline
def ints(): return map(int, input().split())
mod = 1000000007
# endregion ------------------------------------------------------------------------|

def solve(n, a):
    ans = [0] * n
    for i in range(1, n):
        prev_xor = a[i - 1] ^ ans[i - 1]
        ans[i] = prev_xor & ~ a[i]
    return ans
for t in range(int(input())):
    n = int(input())
    a = list(ints())
    print(*solve(n, a))
