Constructing a Special XOR Sequence

You are given an integer n. Your task is to construct a sequence of n distinct positive integers \(\{a_i\}\) such that:

• The bitwise XOR of all elements is equal to \(n\): \(a_1 \oplus a_2 \oplus \cdots \oplus a_n = n\). (Here \(\oplus\) denotes the bitwise XOR operation.)
• The sum of all elements does not exceed \(n^2\): \(\displaystyle\sum_{i=1}^n a_i \le n^2\).

If there is no such sequence, output -1. In case there are multiple answers, you can output any one of them.

Note: This problem is evaluated by Special Judge.

You need to answer T test cases.

inputFormat

The first line contains a single integer T (\(1 \le T \le 10^5\)), the number of test cases.

Each of the next T lines contains a single integer n (\(1 \le n \le 10^9\)).

outputFormat

For each test case, if a valid sequence exists, output a single line containing n space-separated integers \(a_1, a_2, \dots, a_n\) satisfying the conditions. Otherwise, output -1.

Special Judge: Your output will be accepted if it meets all the required conditions.

sample

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