Kurumi just found a particularly nasty cipher on the internet and she needs your help!

The cipher takes the shape of a permutation ~P~ of length ~N~. According to information she got from the dark web, the solution to the cipher revolves around what is known as a ~K~-insert.

Specifically, a ~K~-insert of the integer ~x~ is a two step process:

• Step 1: the integer ~x~ is removed from ~P~.
• Step 2: the integer ~x~ is inserted after the ~K~-th element in the modified ~P~. In particular, if ~K = 0~, it is inserted at the beginning.

A solution ~A~ to the cipher is a sequence of ~K~-inserts that turns ~P~ into the identity permutation. In particular, a ~K~-insert of the integer ~A_i~ is performed as the ~i~-th action.

In the interest of time, Kurumi wants to know the shortest possible solution. Can you help Kurumi find the shortest possible ~A~? To ensure the integrity of your solution, there may be up to ~T~ test cases.

Constraints

~1 \le T \le 10^6~

~1 \le N \le 10^6~

~0 \le K \le N - 1~

The array ~P~ forms a permutation of the integers ~1, \ldots, N~.

The sum of ~N~ over all test cases does not exceed ~10^6~.

Subtask 1 [10%]

~K = 0~

Subtask 2 [90%]

No additional constraints.

Input Specification

The first line contains an integer ~T~, the number of test cases. The remaining ~2T~ lines describe the test cases.

The first line of each test case contains ~2~ integers, ~N~ and ~K~.

The second line of each test case contains ~N~ space-separated integers, representing the permutation ~P~.

Output Specification

For each test case, output two lines.

On the first line, output a single integer ~M~, representing the length of ~A~.

On the second line, output ~M~ space-separated integers, representing the solution ~A~.

If there are multiple possible solutions, output any one of them.

This problem is graded with a standard checker, so if ~M = 0~, you may output an empty line, no line, or a line containing just whitespace.

Scoring

For each case within a test, if your output is ill-formatted or your sequence ~A~ is not a solution, you will receive ~0\%~ of the points for that case.

Otherwise, let ~M'~ be the length of the shortest solution.

• If ~M' < M \leq 2M'~, you will receive ~50\%~ of the points for that case.
• If ~M' = M~, you will receive ~100\%~ of the points for that case.

Your score for a case will be the minimum of the scores of all the tests in the case. Your score for a batch is the minimum of the scores of all of the tests in the batch.

Sample Input

1
4 1
2 3 4 1

Sample Output

2
1 2

Explanation for Sample

After the first ~K~-insert, the permutation becomes ~[2, 1, 3, 4]~.

After the second ~K~-insert, the permutation becomes ~[1, 2, 3, 4]~.

It can be proven that a solution of shorter length does not exist, so this solution would receive ~100\%~ of the points for this case.