A13136. Subset with Zero Sum

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.

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

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