human
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...
Using python3 can you solve the prior task?
 ... Write me a Python program to find the lexicographically minimal sequence y_1, y_2,?
assistant
#Here is Python program to find the lexicographically minimal sequence y_1, y_2, .

# Library Imports
from math import sqrt,ceil,floor
import sys
from collections import Counter,deque
from collections import defaultdict as dd

# Debug Function
# def variablename(variable):
#     for name in globals():
#         if eval(name) == variable:
#             return name
# def debug(x):
#     print(f"{variablename(x)}={x}")


# Code Here

def foo(x):
    x=0


# MultiTestCase

t=int(input())
for tt in range(t):
    
    n=int(input())
    # n,m=map(int,input().split())
    x=list(map(int,input().split()))
    y=[0]
    ans=[x[0]]
    for i in range(1,n):
        z=ans[i-1]&x[i]
        # print(i,z)
        z^=ans[i-1]
        # print(i,z,'xorred')
        y.append(z)
        ans.append(x[i]^y[i])
    print(*y)