Beautiful Sequence

题号：NC256821
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Students from Antarctic Penguin Language School are studying sequence.

We call a sequence $A=(A_1, A_2, \dots, A_n)$ of length $n$ beautiful when all the following conditions are true:

$A_1 \le A_2 \le \dots \le A_n$
For each $A_i$ ( $1\le i\le n$ ), $0\le A_i<2^{30}$ .
For each $1\le i<n$ , $A_i\oplus A_{i+1}=B_i$ , where $B$ is a given sequence, and $\oplus$ represents bitwise XOR.

You need to find the $k$ -th smallest lexicographically legal beautiful sequence $A$ .

输入描述:

Each test contains multiple test cases. The first line contains the number of test cases . The description of the test cases follows.

The first line contains two integers ,  (, ).

The second line contains  integers  ().

It is guaranteed that the sum of  over all test cases does not exceed .

输出描述:

For each test case, output your operations in the following format.

If the number of beautiful sequences is less than , output one line containing an integer .

Otherwise, output one line containing  integers  separated by spaces --- the -th smallest lexicographically legal beautiful sequence.

示例1

输入

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输出

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8 9 11
-1
0 0