## Problem 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. **Don't output any trailing spaces at the end of each line, or you may get an Output Format Error!**

## Sample Input

5 9
7 3
-1 -1

## Sample Output

4 5 3 2 1
1 2 3 4 7 6 5

## Source

Shanghai2004 Preliminary