## MMINPER - Minimum Permutation

Đọc đề đẹp hơn ở:

https://codeforces.com/group/FLVn1Sc504/contest/274506/problem/T

https://codeforces.com/group/FLVn1Sc504/contest/274506/problem/T

English | Vietnamese |

The inversion number of an integer sequence a1, a2, . . . , an is the number of pairs (ai, aj) that satisfy i < j and ai > aj . Given n and the inversion number m, your task is to ﬁnd the smallest permutation of the set { 1, 2, . . . , n } , whose inversion number is exactly m. A permutation a1, a2, . . . , an is smaller than b1, b2, . . . , bn if and only if there exists an integer k such that aj = bj for 1 ≤ j < k but ak < bk.

### Input

The input consists of several test cases. Each line of the input contains two integers n and m. Both of the integers at the last line of the input is −1, which should not be processed. You may assume that 1 ≤ n ≤ 50000 and 0 ≤ m ≤ 1/2n(n − 1). Sample Input 5 9 7 3 -1 -1

### Output

For each test case, print a line containing the smallest permutation as described above, separates the numbers by single spaces. Sample output 4 5 3 2 1 1 2 3 4 7 6 5

Added by: | ~!(*(@*!@^& |

Date: | 2009-02-23 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

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

Resource: | Pre Shanghai 2004 |