Permutation

题号：NC210588
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
Special Judge, 64bit IO Format: %lld

题目描述

You are given a prime number p, you want to find a permutation of numbers $1, 2, \dots, p-1$ , denoted as $x_1, x_2, \dots, x_{p-1}$ , such that for all $i (1\leq i\leq p-2)$ , $x_{i+1}\equiv 2 x_i \pmod p$ or $x_{i+1} \equiv 3x_i \pmod p$ .

输入描述:

The first line contains an integer  indicating the number of test cases.
For each test case, there is one prime number  in the first line.
It's guaranteed that .

输出描述:

If there is no solution for this prime, print '-1'. Otherwise print p-1 integers .

示例1

输入

复制

2
3
5

输出

复制

1 2
1 2 4 3