# POJ2085

Written by    14:00 October 12, 2014

POJ2085

Inversion
 Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 4004 Accepted: 1790

Description

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 <= n(n − 1)/2.

Output

For each test case, print a line containing the smallest permutation as described above, separates the numbers by single spaces.

Sample Input

Sample Output

Source

6 5 7 4 3 2 1 的倒序数就等于 5 7 6 4 3 2 1, 但是根据题意：

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

Category : acmstudy

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