All correct parenthesizations

Given some pairs of corresponding open and close parenthesis, we can use them to build an infinite number of correct parenthesizations. For instance, with the pairs ( ) and [ ], all correct parenthesizations are defined by the grammar $\begin{align*} P & \rightarrow \enspace <\mbox{empty word}> \\ P & \rightarrow \texttt{(} P \texttt{)} P \\ P & \rightarrow \texttt{[} P \texttt{]} P \end{align*}$

Can you generate all correct parenthesizations of a given size?

Input

Input consists of a non-empty string $s$ and a strictly positive even number $n$ . The string $s$ has even size, and includes the corresponding pairs of open and close parenthesis: $s[0]$ with $s[1]$ , $s[2]$ with $s[3]$ , etc.

Output

Print all correct parenthesizations of size $n$ that can be made up with the corresponding open and close parenthesis included in $s$ .

Observation

You can print the parenthesizations in any order.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:26:13.745Z