P10032 "Cfz Round 3" Mex of Sequence

**Please note the special time limit of this problem.** Given a sequence $a$ of length $n$ and an integer $m$. We define one operation as: **simultaneously** replace **each** element $a_i$ in sequence $a$ with the $\operatorname{mex}$ of all elements in sequence $a$ except $a_i$. You need to output the sequence $a$ after performing $m$ operations. Here, the $\operatorname{mex}$ of a sequence is the **smallest natural number that does not appear** in the sequence. For example: - $\operatorname{mex}\{1,2,3\}=0$. - $\operatorname{mex}\{0\}=1$. - $\operatorname{mex}\{1,0,2,4\}=3$. - $\operatorname{mex}\{2,1,3,0,2\}=4$. In particular, when the sequence is empty, its $\operatorname{mex}$ is $0$.

**This problem has multiple test cases.** The first line contains an integer $T$, the number of test cases. Then the test cases follow. For each test case: - The first line contains two integers $n,m$. - The second line contains $n$ integers, representing the given sequence $a$.

For each test case, output one line containing $n$ integers separated by spaces, representing the sequence $a$ after performing $m$ operations.

#### "Sample Explanation #1" For the first test case, since $\operatorname{mex}\{0,1,2\}=3$, $\operatorname{mex}\{1,1,2\}=0$, $\operatorname{mex}\{1,0,2\}=3$, and $\operatorname{mex}\{1,0,1\}=2$, the sequence $a$ after performing $1$ operation is $\{3,0,3,2\}$. #### Constraints Let $\sum n$ be the sum of $n$ within a single test point. For all testdata, $1 \le T \le 1000$, $1 \le n \le 10^6$, $1 \le m \le 10^9$, $0 \le a_i \le 10^9$, and $\sum n \le 10^6$. **You can get the score for this problem only if you pass all test points.** Translated by ChatGPT 5