CF1701D.Permutation Restoration

Monocarp had a permutation $a$ of $n$ integers $1$, $2$, ..., $n$ (a permutation is an array where each element from $1$ to $n$ occurs exactly once).

Then Monocarp calculated an array of integers $b$ of size $n$, where $b_i = \left\lfloor \frac{i}{a_i} \right\rfloor$. For example, if the permutation $a$ is $[2, 1, 4, 3]$, then the array $b$ is equal to $\left[ \left\lfloor \frac{1}{2} \right\rfloor, \left\lfloor \frac{2}{1} \right\rfloor, \left\lfloor \frac{3}{4} \right\rfloor, \left\lfloor \frac{4}{3} \right\rfloor \right] = [0, 2, 0, 1]$.

Unfortunately, the Monocarp has lost his permutation, so he wants to restore it. Your task is to find a permutation $a$ that corresponds to the given array $b$. If there are multiple possible permutations, then print any of them. The tests are constructed in such a way that least one suitable permutation exists.

Monocarp 原本有一个由 $n$ 个整数 $1, 2, \dots, n$ 构成的排列 $a$（即一个每个元素 $1$ 到 $n$ 恰好出现一次的数组）。

接着，Monocarp 计算了一个长度为 $n$ 的整数数组 $b$，其中 $b_i = \left\lfloor \frac{i}{a_i} \right\rfloor$。例如，若排列 $a$ 为 $[2, 1, 4, 3]$，则数组 $b$ 为 $\left[ \left\lfloor \frac{1}{2} \right\rfloor, \left\lfloor \frac{2}{1} \right\rfloor, \left\lfloor \frac{3}{4} \right\rfloor, \left\lfloor \frac{4}{3} \right\rfloor \right] = [0, 2, 0, 1]$。

不幸的是，Monocarp 丢失了他原来的排列，因此他希望将其恢复。你的任务是找出一个与给定数组 $b$ 对应的排列 $a$。如果存在多个可能的排列，则输出任意一个即可。题目保证测试数据中至少存在一个满足条件的排列。

The first line contains a single integer $t$ ($1 \le t \le 10^5$) — number of test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 5 \cdot 10^5$).

The second line contains $n$ integers $b_1, b_2, \dots, b_n$ ($0 \le b_i \le n$).

Additional constrains on the input:

• the sum of $n$ over test cases does not exceed $5 \cdot 10^5$;
• there exists at least one permutation $a$ that would yield this array $b$.

第一行包含一个整数 $t$（$1 \le t \le 10^5$），表示测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 5 \cdot 10^5$）。

第二行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$0 \le b_i \le n$）。

输入的额外约束：

• 所有测试用例的 $n$ 之和不超过 $5 \cdot 10^5$；
• 至少存在一个排列 $a$，能生成该数组 $b$。

For each test case, print $n$ integers — a permutation $a$ that corresponds to the given array $b$. If there are multiple possible permutations, then print any of them.

对于每个测试用例，输出 $n$ 个整数——一个与给定数组 $b$ 对应的排列 $a$。如果存在多个可能的排列，则输出其中任意一个即可。