Restoring Permutation

题意翻译

有一个长度为n的序列$b_1,b_2,...,b_n$，求字典序最小的序列$a_1,a_2,...a_{2n}$，使得$b_i=min(a_{2i-1},a_{2i})$，若无解，输出数字$-1$。

题目描述

You are given a sequence $ b_1, b_2, \ldots, b_n $ . Find the lexicographically minimal permutation $ a_1, a_2, \ldots, a_{2n} $ such that $ b_i = \min(a_{2i-1}, a_{2i}) $ , or determine that it is impossible.

输入输出格式

输入格式

Each test contains one or more test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). The first line of each test case consists of one integer $ n $ — the number of elements in the sequence $ b $ ( $ 1 \le n \le 100 $ ). The second line of each test case consists of $ n $ different integers $ b_1, \ldots, b_n $ — elements of the sequence $ b $ ( $ 1 \le b_i \le 2n $ ). It is guaranteed that the sum of $ n $ by all test cases doesn't exceed $ 100 $ .

输出格式

For each test case, if there is no appropriate permutation, print one number $ -1 $ . Otherwise, print $ 2n $ integers $ a_1, \ldots, a_{2n} $ — required lexicographically minimal permutation of numbers from $ 1 $ to $ 2n $ .

输入输出样例

输入样例 #1

5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8

输出样例 #1

1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10