SP3933 MMINPER - Minimum Permutation

[English](/problems/MMINPER/en/) [Vietnamese](/problems/MMINPER/vn/) ``` 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. ```

``` 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 ```

``` 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 ```