growing Sequence

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). 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.

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

inputFormat

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.

outputFormat

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

样例

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

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