Bob likes playing with permutations.Alice asks him to play a game.She gave him two integers n and x.Now, she asks Bob to find the x^th ranked permutation of length n.

A permutation of length n is a sequence of size n consisting of n distinct integers in the range [1, n].

Input Format

The only line of the input contains 2 space separated integers n and x.

Output Format

Print n space separated integers which represent x^th ranked permutation.

Constraints

1<=n<=18

1<=x<=10¹⁸

Note : It is guaranteed that answer exists for the given input.