From one to en (3) P69756

Write a program that prints all the permutations of $\{ 1, \dots, n \}$ with $k$ inversions, for a given $n$ and $k$. An inversion is a pair of elements $x$ and $y$ such that $x > y$ and such that $x$ appears before $y$ in the permutation.

Input

Input consists of two natural numbers $n$ and $k$, such that $n \ge 1$ and $0 \le k \le n(n - 1)/2$.

Output

Print all the permutations of $\{ 1, \dots, n \}$ with $k$ inversions.

Information about the checker

You can print the solutions to this exercise in any order.

Hint

Here, a very simple algorithm may be too slow.