[Solution] Xor Permutation CodeChef Solution

[Solution] Xor Permutation CodeChef Solution

Chef has received a challenge for which he needs your help.

Given N$N$, find a permutation P$P$ of numbers (1,2,…,N)$(1,2,\dots ,N)$ such that:

• Pi⊕Pi+1≠Pi+2 , where (1≤i≤N−2)$P_i\oplus P_{i+1}\ne P_{i+2}\text{ , where }(1\le i\le N-2)$. Here ⊕$\oplus$ denotes the bitwise XOR operation.

If multiple such permutations exist, print any. If no such permutation exists, print −1$-1$.

Note that, a permutation of length N$N$ is a sequence of N$N$ integers P=(P1,P2,…,PN)$P=(P_1,P_2,\dots ,P_N)$ such that every integer from 1$1$ to N$N$ (inclusive) appears in it exactly once. For example, (2,5,4,1,3)$(2,5,4,1,3)$ is a permutation of length 5$5$ while (2,5,2,1,3)$(2,5,2,1,3)$ is not.

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Input Format

• First line will contain T$T$, number of test cases. Then the test cases follow.
• Each test case contains of a single integer as input, N$N$ - the length of the required permutation.

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Output Format

For each test case, output in a new line, N$N$ space-separated integers, denoting a permutation satisfying the condition.
If multiple such permutations exist, print any. If no such permutation exists, print −1$-1$.

Constraints

• 1≤T≤500$1\le T\le 500$
• 3≤N≤105$3\le N\le {10}^5$
• Sum of N$N$ over all test cases does not exceed 2⋅105