Background

Kevin solved this problem at a glance.

Problem Description

Given a positive integer $n$, construct a sequence $a_1,a_2,\dots,a_n$ of length $n$ consisting of non-negative integers, such that:

• For all $1\le i\le n$, we have $0\le a_i\le m$.
• $a_1\oplus a_2\oplus\dots\oplus a_n=k$, where $\oplus$ denotes the bitwise XOR operation.

Or determine that no such sequence exists.

Input Format

This problem contains multiple test cases.

The first line of the input contains a positive integer $T$, denoting the number of test cases.

For each test case, the input contains one line with three non-negative integers $n,k,m$.

Output Format

For each test case, output one line with $-1$ to indicate that no such sequence exists.

Otherwise, output $n$ non-negative integers separated by spaces, representing the sequence you construct. If there are multiple valid answers, you only need to output any one of them.

5
1 2 2
2 3 10
2 11 8
20 200000 99999
11 191 9810

2 
4 7 
8 3 
-1
191 191 191 191 191 191 191 191 191 191 191 

Hint

[Sample Explanation]

For the $1$st test case, there is one and only one sequence that satisfies the conditions.

For the $2$nd test case, since $4\oplus 7=3$ and $4,7\le10$, this is a valid answer. Similarly, the sequence $(2,1)$ is also a valid answer.

For the $4$th test case, it can be proven that there is no sequence that meets the requirements.

[Constraints]

Let $\sum n$ be the sum of all $n$ values within a single test point.

For all testdata, it is guaranteed that $1\le T\le 1~000$, $1\le n\le 2\cdot10^5$, $0\le m,k\le 10^8$, and $\sum n\le 2\cdot10^5$.

[Subtasks]

This problem uses bundled test cases.

• Subtask 1 (18 pts): $k\le m$.
• Subtask 2 (82 pts): No additional constraints.

Translated by ChatGPT 5