## Problem B: Enumerating Brackets

A balanced bracket sequence is a string consisting only of the characters "`(`" (opening brackets) and "`)`" (closing brackets) such that each opening bracket has a "matching" closing bracket, and vice versa. For example, "`(())()`" is a balanced bracket sequence, whereas "`(())(()`" and "`())(()`" are not.

Given two bracket sequences A and B of the same length, we say that A is lexicographically smaller than B (and write A < B) if:

1. A and B differ in at least one position, and
2. A has a "`(`", and B has a "`)`" in the left-most position in which A and B differ

For example "`(())()`" < "`()()()`" because they first differ in the second position from the left, and the first string has an "`(`" in that position, whereas the second string has a "`)`". For a given length N, the "<" operator defines an ordering on all balanced bracket sequences of length N. For example, the ordering of the sequences of length 6 is:

1. `((()))`
2. `(()())`
3. `(())()`
4. `()(())`
5. `()()()`

Given a length N and a positive integer M, your task is to find the Mth balanced bracket sequence in the ordering.

### Input Specification

You will be given an even integer N (2 ≤ N ≤ 2000), and a positive integer M. It is guaranteed that M will be no more than 1018 and no more than the number of balanced bracket sequences of length N (whichever is smaller).

### Output Specification

Output the Mth balanced bracket sequence of length N, when ordered lexicographically.

### Sample Input

``6 4``

### Output for Sample Input

``()(())``

Deon Nicholas