P9227 XOR Product

$\texttt{id: 4d7e}$ Little H learned about the XOR operation in class. For two non-negative integers $x, y$, their **XOR** is defined as follows: treat them as binary numbers, and for each bit position compute the result bit by bit: - If the bits of $x$ and $y$ at this position are different, the result bit is $1$. - If the bits of $x$ and $y$ at this position are the same, the result bit is $0$. The XOR of $x$ and $y$ is written as $x \operatorname{xor} y$ or $x \oplus y$. In C++, you can use `x ^ y` to get the XOR value of $x$ and $y$. Also, the XOR of multiple numbers is called the **XOR sum**.

Little H also learned that the **XOR product** of a sequence $a$ of length $n$ is a sequence $b$ of the same length, where $b_i$ equals the XOR sum of all elements in $a$ except $a_i$, that is, $$b_i = \bigoplus \limits_{j = 1}^{n} [j\ne i] a_j$$ For example, the XOR product of the sequence $\{1, 2, 3, 4\}$ is $\{5, 6, 7, 0\}$. A **XOR product transformation** means replacing a sequence with its XOR product. Since the sequence length does not change after a transformation, the XOR product transformation can be applied multiple times in a row. Now, Little H has a sequence $a$ of length $n$. He wants you to help him compute the sequence obtained after applying $k$ XOR product transformations to $a$.

**This problem contains multiple test cases within a single test point.** The first line contains an integer $T$, the number of test cases. For each test case: The first line contains two integers $n, k$. The second line contains $n$ integers $a_1, a_2, \cdots, a_n$.

For each test case: Output one line with $n$ integers, representing the sequence obtained after applying $k$ XOR product transformations to sequence $a$.

### Explanation for Sample 1 This sample is exactly the example given in the statement. ### Explanation for Sample 2 After the 1st XOR product transformation: $\{0,0,0,1\}\to\{1,1,1,0\}$; After the 2nd XOR product transformation: $\{1,1,1,0\}\to\{0,0,0,1\}$. ### Constraints For $100\%$ of the testdata, $1 \le T \le 10$, $2 \le n \le 10^5$, $1 \le k \le 10^{18}$, $0 \le a_i < 2^{32}$. | Test Point ID | $n\leq$ | $k \leq$ | Special Property | | :----------: | :----------: | :----------: | :-----------: | | $1 \sim 3$ | $100$ | $100$ | | | $4 \sim 5$ | $1000$ | $1000$ | | | $6 \sim 7$ | $3$ | $10^{18}$ | | | $8 \sim 10$ | $10^5$ | $3$ | | | $11 \sim 13$ | $10^5$ | $10^{18}$ | The XOR sum of all numbers in $a$ is $0$ | | $14 \sim 15$ | $10^5$ | $10^{18}$ | $n$ is odd | | $16 \sim 17$ | $10^5$ | $10^{18}$ | $n$ is even | | $18 \sim 20$ | $10^5$ | $10^{18}$ | | ### Notes In C++, for the range $0 \le x < 2^{32}$, you can: - Use `unsigned int x` to define it. - Use `cin >> x` or `scanf("%u", &x)` for input. - Use `cout