Not-So-Long Increasing Subsequence

Let $N, K$ be positive integers satisfying $K \leq N$. Busy Beaver has a permutation1 $a\_1, \ldots, a\_N$ of $1, \dots, N$. A length $K$ subsequence2 of $a\_1, \ldots, a\_N$ given by $b\_1, \ldots, b\_K$ is interesting if the longest increasing3 subsequence of $b\_1, \dots, b\_K$ has length at most $\frac{K+1}{2}$.

Determine whether Busy Beaver's permutation has an interesting subsequence of length $K$, and if it exists, provide such an example of an interesting subsequence.

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1A permutation of length $N$ is an array consisting of $N$ distinct integers from $1$ to $N$ in arbitrary order. For example, $\[2,3,1,5,4]$ is a permutation, but $\[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $\[1,3,4]$ is also not a permutation ($N=3$ but there is $4$ in the array).

2A sequence $a$ is a subsequence of a sequence $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements.

3A sequence $a\_1, \dots, a\_m$ is increasing if $a\_1 < a\_2 < \dots < a\_{m-1} < a\_m$. For instance, $\[1, 2, 5]$ is increasing while $\[2, 5, 1]$ is not.

Each test contains multiple test cases. The first line of input contains a single integer $T$ $(1 \leq T \leq 10^5)$, the number of test cases. The description of each test case follows.

The first line of each test case contains two space-separated integers $N, K$ ($1 \leq K \leq N \leq 2 \cdot 10^5$).

The second line of each test case contains $N$ integers $a\_1, a\_2, \ldots, a\_N$ ($1 \leq a\_i \leq N$, $a\_i$ pairwise distinct) --- Busy Beaver's permutation.

It is guaranteed that the sum of $N$ across all test cases is no more than $2 \cdot 10^5$.

For each test case, output "YES" (without quotes) if there exists an interesting subsequence, and "NO" (without quotes) otherwise. You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).

Then, if you responded with "YES", print a second line consisting of $K$ space-separated integers $i\_1, \dots, i\_K$ ($1 \leq i\_1 < \dots < i\_K \leq n$), the indices of the permutation such that $a\_{i\_1}, \dots, a\_{i\_K}$ is an interesting subsequence. If there are multiple possible solutions, print any of them.

In the first test case, the subsequence $\[a\_2, a\_3] = \[2, 1]$ has two longest increasing subsequences $\[2]$ and $\[1]$, each of which has length at most $\frac{2 + 1}{2} = \frac 32.$ It is therefore an interesting subsequence.

In the second test case, the subsequence $\[a\_5, a\_6, a\_7] = \[7, 2, 6]$ has a unique longest increasing subsequence given by $\[2, 6]$, which has length at most $\frac{3 + 1}{2} = 2.$ It is therefore an interesting subsequence.

In the third test case, the only subsequence of length $8$ is the entire sequence $\[a\_1, \dots, a\_8] = \[4, 5, 6, 7, 8, 1, 2, 3]$. The longest increasing subsequence of this sequence is $\[4, 5, 6, 7, 8]$. As its length is greater than $\frac{8 + 1}{2} = \frac 92$, there is no interesting subsequence.