Mocha and Hiking

Description:

Input:

Each test contains multiple test cases.

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 20$$$) — the number of test cases. Each test case consists of two lines.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^4$$$) — indicates that the number of villages is $$$n+1$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 1$$$). If $$$a_i=0$$$, it means that there is a road from village $$$i$$$ to village $$$n+1$$$. If $$$a_i=1$$$, it means that there is a road from village $$$n+1$$$ to village $$$i$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.

Output:

For each test case, print a line with $$$n+1$$$ integers, where the $$$i$$$-th number is the $$$i$$$-th village they will go through. If the answer doesn't exist, print $$$-1$$$.

If there are multiple correct answers, you can print any one of them.

Sample Input:

2
3
0 1 0
3
1 1 0

Sample Output:

1 4 2 3 
4 1 2 3 

Note:

In the first test case, the city looks like the following graph:

So all possible answers are $$$(1 \to 4 \to 2 \to 3)$$$, $$$(1 \to 2 \to 3 \to 4)$$$.

In the second test case, the city looks like the following graph:

So all possible answers are $$$(4 \to 1 \to 2 \to 3)$$$, $$$(1 \to 2 \to 3 \to 4)$$$, $$$(3 \to 4 \to 1 \to 2)$$$, $$$(2 \to 3 \to 4 \to 1)$$$.