Box

Description:

Input:

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 $$$10^5$$$.

Output:

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.

Sample Input:

4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1

Sample Output:

1 3 4 5 2 
-1
2 1 
1 

Note:

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.