Task Scheduler

Problem Description

ByteCompany has a server cluster with $m$ workers, $k$ of which are somehow disconnected. The task scheduler have just received $n$ tasks, and the $i$-th task needs to be executed on $t_i$ workers. For an executive order of $p_1 ,p_2 , \ldots p_n$, the task scheduler will assign workers for them respectively. Specifically, for the $i$-th task $p_i$, the scheduler will select $t_{p_i}$ workers randomly from all workers which hasn't been assigned tasks at this moment. Each of those free workers share a universal equal probability to be selected. Note that disconnected workers may also be selected. In this scenario, the current scheduling will be considered as a failure and retry automatically and immediately. Only when the scheduling of the current task is successful, the next task will be proceeded. Now you need to find an optimal executive order of $p_1 ,p_2 , \ldots p_n$ to minimize the expected amount of the scheduling process. We guarantee that the amount of connected workers is enough to finish all scheduling.

Input

The input contains several test cases, and the first line contains a single integer $T$ ($1 \le T \le 100$), the number of test cases. For each test case, the first line contains three integers $n$ ($1 \le n \le 100$), $m$ ($n \le m \le 10\,000$) and $k$ ($0 \le k \le m - n$): the number of tasks, the total number of workers and the number of disconnected workers. The following line contains $n$ positive integers $t_1, t_2, t_3, \ldots, t_n$ ($n \le \sum_{i=1}^{n}t_i \le m - k$), describing the number of needed worker for each task.

Output

For each test case, output $n$ integers $p_1 ,p_2 , \ldots, p_n$ on a single line representing the order of tasks to be scheduled. If there are multiple solutions, output the lexicographically smallest one.

Sample Input

2
2 4 1
1 2
3 3 0
1 1 1

Sample Output

2 1
1 2 3

Source

2020 Multi-University Training Contest 10