D. Co-growing Sequencetime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA sequence of non-negative integers a_1, a_2, \dots, 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). 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, \dots, x_n and y_1, y_2, \dots, y_n. Let's call this pair of sequences co-growing if the sequence x_1 \oplus y_1, x_2 \oplus y_2, \dots, x_n \oplus y_n is growing where \oplus denotes bitwise XOR.You are given a sequence of integers x_1, x_2, \dots, x_n. Find the lexicographically minimal sequence y_1, y_2, \dots, y_n such that sequences x_i and y_i are co-growing.The sequence a_1, a_2, \dots, a_n is lexicographically smaller than the sequence b_1, b_2, \dots, b_n if there exists 1 \le k \le n such that a_i = b_i for any 1 \le i < k but a_k < b_k.InputThe first line contains an integer t (1 \le t \le 10^4). Then t test cases follow.The first line of each test case contains an integer n (1 \le n \le 2 \cdot 10^5) — length of the sequence x_i.The second line contains n integers x_1, x_2, \dots, x_n (0 \le 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 \cdot 10^5.OutputFor each test case, print n integers y_1, y_2, \dots, y_n (0 \le y_i < 2^{30}) — lexicographically minimal sequence such that such that it's co-growing with given sequence x_i.ExampleInput
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 

5
4
1 3 7 15
4
1 2 4 8
5
1 2 3 4 5
4
11 13 15 1
1
0

0 0 0 0  0 1 3 7  0 1 0 3 2  0 2 0 14  0  
['bitmasks', 'constructive algorithms', 'greedy', '*1300']