Brackets#5482
Consider all valid bracket sequences of length . These sequences are arranged in lexicographical order (an opening bracket is considered less than a closing bracket). Each sequence is numbered starting from .
Your task is to find the -th sequence in this ordering.
The first line contains the integer (1 \leq N \leq 100). The second line contains a natural number (1 \leq K \leq 10^{1000}+255), which specifies the sequence number to find.
Output a single line containing the -th valid bracket sequence of length . The output should not contain any spaces. If there are fewer than sequences of length , output "No solution for this testcase." (without quotes).
Example 1