VSHEOM-43#5153
In the distant past, at the dawn of era , the children of LKSH constructed the Huge School Electronic Computing Machine, or HSECM-43. Today, many generations later, a new group of LKSH children has uncovered this technological legacy of their ancestors.
Recently, they have been studying correct bracket sequences consisting of round and square brackets. To test their knowledge, they decided to list the first correct bracket sequences of length in lexicographical order. Fortunately, the rediscovered supercomputer can solve this problem. However, it turned out that the creators of the HSECM-43 had a unique interpretation of lexicographical order. Specifically, they considered brackets to be ordered as illustrated below:
Your task is to determine what the LKSH children saw on the HSECM-43 screen.
The input consists of two numbers: (1 \leq N \leq 100) and (1 \leq K \leq \min(10000, C_{2N}^N)), where C_{2N}^N is the binomial coefficient.
Output lines, each containing one of the first correct bracket sequences of length , composed of round and square brackets, listed in lexicographical order corresponding to the specified order.
Example 1