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