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Even-Odd XOR

1000ms 262144K

Description:

Given an integer $$$n$$$, find any array $$$a$$$ of $$$n$$$ distinct nonnegative integers less than $$$2^{31}$$$ such that the bitwise XOR of the elements on odd indices equals the bitwise XOR of the elements on even indices.

Input:

The first line of the input contains an integer $$$t$$$ ($$$1 \leq t \leq 629$$$) — the number of test cases.

Then $$$t$$$ lines follow, each containing a single integer $$$n$$$ $$$(3 \leq n \leq 2\cdot10^5)$$$ — the length of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output:

For each test case, output one line containing $$$n$$$ distinct integers that satisfy the conditions.

If there are multiple answers, you can output any of them.

Sample Input:

7
8
3
4
5
6
7
9

Sample Output:

4 2 1 5 0 6 7 3
2 1 3
2 1 3 0
2 0 4 5 3
4 1 2 12 3 8
1 2 3 4 5 6 7
8 2 3 7 4 0 5 6 9

Note:

In the first test case the XOR on odd indices is $$$4 \oplus 1 \oplus 0 \oplus 7 = 2$$$ and the XOR on even indices is $$$2 \oplus 5 \oplus 6 \oplus 3= 2$$$.

Informação

Codeforces

Provedor Codeforces

Código CF1722G

Tags

bitmasksconstructive algorithmsgreedy

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Datas 09/05/2023 10:31:10

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