## LEXBRAC - Bracket Sequence

Correct Bracket Sequence (CBS) is a sequence that can be obtained through following rules:

1) An empty string is the CBS.

2) If A is a CBS, then B = (A) is also a CBS.

3) If A is a CBS, then B = [A] is also a CBS.

4) If A and B are CBS, then C = AB is also a CBS.

Length of the CBS is the number of brackets in it, and this number is always even.

Assume that '(' < ')' < '[' < ']'.

CBS a1a2 ... an is lexicografically smaller than the CBS b1b2 ... bn if and only if there exists an integer i, i <= n, so that aj=bj, for each j, 1 <= j < i and ai < bi.

### Illustration

Enumerate all CBS length 4 in lexicographical order: (()), ()(), ()[], ([]), [()], [[]], [](), [][].

### Task

Your task is to find k-th CBS with length n in lexicographical order

### Input

Contains 2 integers n (2..250) and k (1..10^120)

### Output

Print the k-th CBS with length n in lexicographical order

### Example

Input:4 3Output:()[]

Added by: | Chinh Nguyen |

Date: | 2008-01-10 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |