CF2137D Replace with Occurrences

Given an array $$$a$$$, let $$$f(x)$$$ be the number of occurrences of $$$x$$$ in the array $$$a$$$. For example, when $$$a=\[1,2,3,1,4\]$$$, then $$$f(1)=2$$$ and $$$f(3)=1$$$. You have an array $$$b$$$ of size $$$n$$$. Please determine if there is an array $$$a$$$ of size $$$n$$$ such that $$$f(a\_i)=b\_i$$$ for all $$$1 \\leq i \\leq n$$$. If there is one, construct it.

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\le t \\le 10^4$$$). The description of the test cases follows. The first line of each test case contains an integer $$$n$$$ ($$$1 \\leq n \\leq 2\\cdot 10^5$$$). The second line contains $$$n$$$ integers $$$b\_1,b\_2,\\ldots,b\_n$$$ ($$$1 \\leq b\_i \\leq n$$$). It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\\cdot 10^5$$$.

For each test case, output $$$-1$$$ if there is no valid array $$$a$$$. Otherwise, print the array $$$a$$$ of $$$n$$$ integers on a new line. The elements should satisfy $$$1 \\leq a\_i \\leq n$$$.

In the first test case, it can be shown that no array matches the requirement. In the second test case, $$$4$$$, $$$5$$$, $$$6$$$ appear $$$1,2,3$$$ times respectively. Thus, the output array is correct as $$$f(4),f(5),f(5),f(6),f(6),f(6)$$$ are $$$1,2,2,3,3,3$$$ respectively.