P7938 「Wdcfr-1」Beautiful Array

In this problem, we define a sequence of `(` and `)` as a "bracket sequence". The definition of *Regular Bracket Sequence* is as follows: 1. `()` is a Regular Bracket Sequence. 1. If `A` is a Regular Bracket Sequence, then `(A)` is also a Regular Bracket Sequence. 1. If `A` and `B` are Regular Bracket Sequences, then `AB` is also a Regular Bracket Sequence. For example: `()`, `(())`, and `()()` are all Regular Bracket Sequences, but `)(`, `()(` are not. In particular, an empty sequence is **not** a Regular Bracket Sequence sequence in this problem. Now ~~cute~~ Ran gives you a bracket sequence $s$ of length $n$. She wants you to construct $2\cdot m$ **strictly increasing** arrays. Let us denote them as $p_1,p_2,\cdots,p_{2 m}$ (you can leave any of them empty). You need to ensure that all integers between $1\sim n$ appear **exactly once** in these arrays. An array $p_i=\{r_1,r_2,\cdots,r_k\}$ is *Beautiful* if $\{s_{r_1},s_{r_2},\cdots,s_{r_k}\}$ is a Regular Bracket Sequence. Ran wonders whether it is possible to construct these arrays so that at least $m$ of the $2\cdot m$ arrays are "beautiful arrays".

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### Explanation For the first test case, we can construct $p_1=\{1,2\}$ and $ p_2=\{\}$. So $p_1$ is a "beautiful array". For the second test case, it is obvious that we cannot use two numbers to construct $99$ beautiful arrays. ### Constraints $1\le T,n,m\le 200$.