From one to en (3) P69756

Write a program that prints all the permutations of { 1, …, 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 ≥ 1 and 0 ≤ k ≤ n(n − 1)/2.

Output

Print all the permutations of { 1, …, 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.