Background

Problem Number: $\textit{23}$

As everyone knows, Shameimaru Aya and Cirno are good friends. However, Aya is a powerful youkai and very smart, while Cirno is a fool. To improve Cirno’s IQ, Aya gave Cirno a simple problem.

Problem Description

For a sequence $p$ of length $l$, define $S(p)$ as the bitwise XOR sum of all elements, where $\oplus$ denotes the bitwise XOR operation.

Given integers $s, m$, determine whether it is possible to construct a sequence $a$ of length $n$ (you may choose $n$) such that:

• $1 \le n \le m$.
• $1 \le a_i \le s$.
• $S(a) = 0$.
• $a_1 + a_2 + \cdots + a_n = s$.

Construct any valid solution, or report that no solution exists.

Input Format

This problem contains multiple test cases.

• The first line contains an integer $T$, the number of test cases.
• The next $T$ lines each contain two integers $s, m$, representing one query.

Output Format

• Output a total of $T$ lines.
• For each test case:
  • If there is a solution, first output an integer $n$, then output $n$ integers representing $a$.
  • If there is no solution, output a single integer $-1$ on one line.

2
14 9
3 3

3 3 5 6
-1

Hint

Sample Explanation

• For test case $1$, it is easy to see that $3 \oplus 5 \oplus 6 = 0$ and $3 + 5 + 6 = 14$, which satisfies the requirements.
• For test case $2$, the sequences $\{3\}$, $\{1,2\}$, and $\{1,1,1\}$ all do not satisfy the requirements, so there is no solution.

Constraints and Notes

For $100\%$ of the testdata, $1 \le s \le 10^{18}$, $1 \le m$, and $1 \le \sum m \le 10^6$.

Friendly reminder: you may need to use faster I/O.

Translated by ChatGPT 5