Background

Five top experts have gathered here, and sparks of ideas collide fiercely. Soon, PFLOI Round 1 is ready.

It begins...

Problem Description

A new journey has begun: Zhili has set out to look for bananas. There are a total of $n$ bananas on the road, numbered from $1$ to $n$.

Seeing such delicious food, Zhili is very excited. However, Zhili does not want to eat too much or too little, so it will eat exactly $m$ bananas.

Zhili is very picky. It will only be satisfied if the XOR sum of the indices of the $m$ bananas it eats is exactly $2^{\lfloor\log_2 n\rfloor+1}-1$. Please help find which bananas it should eat to make it satisfied.

If Zhili's requirement cannot be satisfied no matter what, please output -1.

Formal statement:

Please choose $m$ numbers from $1$ to $n$ such that their XOR sum is exactly $2^{\lfloor\log_2 n\rfloor+1}-1$. If there is no solution, output -1.

Input Format

This problem has multiple test cases.

The first line contains an integer $T$, meaning there are $T$ test cases in total.

For each test case, each line contains two integers $n$ and $m$, with meanings as described in the statement.

Output Format

For each test case, if there is a solution, output one line with $m$ integers, representing the $m$ numbers you choose. If there is no solution, output -1.

This problem uses Special Judge. If there are multiple possible solutions, you may output any one of them.

7
5 2
6 6
7 6
8 3
9 3
10 1
7 4

3 4
1 6 2 4 3 5 
1 2 3 4 5 6
8 6 1
8 1 6
-1
3 5 6 7

Hint

This problem does not use bundled tests.

Constraints: For all testdata, $1\le m\le n\le10^6$, $1\le\sum n,T\le10^6$.

Translated by ChatGPT 5