Inversion

Time Limit: 1 Second    Memory Limit: 32768 KB

The inversion number of an integer sequence a₁, a₂, ... , a_n is the number of pairs (a_i, a_j) that satisfy i < j and a_i > a_j. 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, ... , a_n is smaller than b₁, b₂, ... , b_n if and only if there exists an integer k such that a_j = b_j for 1 <= j < k but a_k < b_k.

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 <= 1/2*n*(n-1).

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 'Presentation Error'!

Sample Input

5 9
7 3
-1 -1

Sample Output

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

Submit

Source: Asia 2004, Shanghai (Mainland China), Preliminary