All correct parenthesizations P48260


Statement
 

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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

     
P →   <empty word>          
P → ( P ) P          
P → [ P ] P          

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.

Public test cases
  • Input

    () 6
    

    Output

    ()()()
    ()(())
    (())()
    (()())
    ((()))
    
  • Input

    {}()[] 2
    

    Output

    {}
    ()
    []
    
  • Input

    []() 4
    

    Output

    [][]
    ()[]
    []()
    ()()
    [[]]
    ([])
    [()]
    (())
    
  • Information
    Author
    Salvador Roura
    Language
    English
    Official solutions
    C++
    User solutions
    C++ Haskell
    Event
    Tretzè Concurs de Programació de la UPC - Semifinal
    Date
    2015-07-01