CF1227B.Box

Permutation $p$ is a sequence of integers $p=[p_1, p_2, \dots, p_n]$ , consisting of $n$ distinct (unique) positive integers between $1$ and $n$ , inclusive. For example, the following sequences are permutations: $[3, 4, 1, 2]$ , $[1]$ , $[1, 2]$ . The following sequences are not permutations: $[0]$ , $[1, 2, 1]$ , $[2, 3]$ , $[0, 1, 2]$ .

The important key is in the locked box that you need to open. To open the box you need to enter secret code. Secret code is a permutation $p$ of length $n$ .

You don't know this permutation, you only know the array $q$ of prefix maximums of this permutation. Formally:

• $q_1=p_1$ ,
• $q_2=\max(p_1, p_2)$ ,
• $q_3=\max(p_1, p_2,p_3)$ ,
• ...
• $q_n=\max(p_1, p_2,\dots,p_n)$ .

You want to construct any possible suitable permutation (i.e. any such permutation, that calculated $q$ for this permutation is equal to the given array).

The first line contains integer number $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the input. Then $t$ test cases follow.

The first line of a test case contains one integer $n$ $(1 \le n \le 10^{5})$ — the number of elements in the secret code permutation $p$ .

The second line of a test case contains $n$ integers $q_1, q_2, \dots, q_n$ $(1 \le q_i \le n)$ — elements of the array $q$ for secret permutation. It is guaranteed that $q_i \le q_{i+1}$ for all $i$ ( $1 \le i < n$ ).

The sum of all values $n$ over all the test cases in the input doesn't exceed $10^5$ .

For each test case, print:

• If it's impossible to find such a permutation $p$ , print "-1" (without quotes).
• Otherwise, print $n$ distinct integers $p_1, p_2, \dots, p_n$ ( $1 \le p_i \le n$ ). If there are multiple possible answers, you can print any of them.

In the first test case of the example answer $[1,3,4,5,2]$ is the only possible answer:

• $q_{1} = p_{1} = 1$ ;
• $q_{2} = \max(p_{1}, p_{2}) = 3$ ;
• $q_{3} = \max(p_{1}, p_{2}, p_{3}) = 4$ ;
• $q_{4} = \max(p_{1}, p_{2}, p_{3}, p_{4}) = 5$ ;
• $q_{5} = \max(p_{1}, p_{2}, p_{3}, p_{4}, p_{5}) = 5$ .

It can be proved that there are no answers for the second test case of the example.