Description

For subsets of $N=\{1,2,\cdots,n\}$, define a relation called "less than":

Let $S1=\{X_1,X_2,\cdots,X_i\}$, $(X_1<X_2<\cdots<X_i)$, $S2=\{Y_1,Y_2,\cdots,Y_j\}$, $(Y_1<Y_2<\cdots<Y_j)$. If there exists a $k$, $(0\leq k\leq\min(i,j))$, such that $X_1=Y_1,\cdots,X_k=Y_k$, and $k=i$ or $X_{k+1}<Y_{k+1}$, then $S1$ is said to be "less than" $S2$.

Your task is, for any $n$ $(n\leq31)$ and $k$ $(k<2^n)$, to find the $k$-th smallest subset.

Input Format

The input file contains a single line with two natural numbers, $n$ and $k$, separated by a space.

Output Format

Output a single line listing the elements of the subset in increasing order. Output $0$ for the empty set.

3 4

1 2 3

Hint

Translated by ChatGPT 5