Co-growing Sequence

A 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 $$$a_k < b_k$$$.