#P1270G. Subset with Zero Sum

    ID: 1429 Type: RemoteJudge 2000ms 256MiB 尝试: 9 已通过: 3 难度: 10 上传者: 标签>constructive algorithmsdfs and similargraphsmath*2700

Subset with Zero Sum

Description

You are given $n$ integers $a_1, a_2, \dots, a_n$, such that for each $1\le i \le n$ holds $i-n\le a_i\le i-1$.

Find some nonempty subset of these integers, whose sum is equal to $0$. It can be shown that such a subset exists under given constraints. If there are several possible subsets with zero-sum, you can find any of them.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^6$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n \le 10^6$).

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($i-n \le a_i \le i-1$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.

For each test case, output two lines.

In the first line, output $s$ ($1\le s \le n$) — the number of elements in your subset.

In the second line, output $s$ integers $i_1, i_2, \dots, i_s$ ($1\le i_k \le n$). All integers have to be pairwise different, and $a_{i_1} + a_{i_2} + \dots + a_{i_s}$ has to be equal to $0$. If there are several possible subsets with zero-sum, you can find any of them.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^6$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n \le 10^6$).

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($i-n \le a_i \le i-1$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.

Output

For each test case, output two lines.

In the first line, output $s$ ($1\le s \le n$) — the number of elements in your subset.

In the second line, output $s$ integers $i_1, i_2, \dots, i_s$ ($1\le i_k \le n$). All integers have to be pairwise different, and $a_{i_1} + a_{i_2} + \dots + a_{i_s}$ has to be equal to $0$. If there are several possible subsets with zero-sum, you can find any of them.

Samples

2
5
0 1 2 3 4
4
-3 1 1 1
1
1 
4
1 4 3 2

Note

In the first example, we get sum is $a_1 = 0$.

In the second example, we get sum is $a_1 + a_4 + a_3 + a_2 = 0$.