B. Boxtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPermutation 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).InputThe 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.OutputFor 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. ExampleInput
4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1
Output
1 3 4 5 2 
-1
2 1 
1 
NoteIn 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.
4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1

1 3 4 5 2  -1 2 1  1  
['constructive algorithms', '*1200']