[Solution] Permutation AND CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Permutation AND CodeChef Solution | CodeChef Problem Solution 2022

Chef's last task in his internship requires him to construct 2$2$ permutations, each having length N$N$, such that the bitwise AND of each pair of elements at every index is the same.

Formally, if the permutations are A$A$ and B$B$, then, the value Ai&Bi$A_i\mathrm{\&}{B}_i$ must be constant over all 1≤i≤N$1\le i\le N$.

Help Chef by providing him 2$2$ such permutations. If it is not possible to construct such permutations, print −1$-1$ instead.

Input Format

• First line will contain T$T$, number of test cases. Then the test cases follow.

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• Each test case contains of a single line of input, a single integer N$N$ denoting the size of the required permutations.

Output Format

• If there are valid permutations that satisfy the required condition, then:
• In the first line, output N$N$ space-separated integers denoting the permutation A$A$.
• In the second line, output N$N$ space-separated integers denoting the permutation B$B$.

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• If there is no valid pair of permutations, print -1 in a single line.

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 1≤N≤105$1\le N\le {10}^5$
• Sum of N$N$ over all test cases does not exceed 2⋅105$2\cdot {10}^5$